We provide motion in a plane practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on motion in a plane skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of motion in a plane Questions

Question No | Questions | Class |
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1 | The velocity of projection of a projectile is given by : ( vec{u}=5 hat{i}+10 hat{j} . ) Range is: A ( .2 m ) в. ( 4 m ) ( c .6 m ) D. ( 10 m ) | 11 |

2 | A particle is projected upwards from the roof of a tower ( 60 m ) high with velocity ( 20 m / s . ) Find the average speed. | 11 |

3 | When a man stands on a moving escalator he goes up in ( 40 s ) and when he walked up the moving escalator he goes up in 20 s. The man walk up the stationary escalator in a time of: ( mathbf{A} cdot 60 ) B. ( 40 s ) ( c cdot 20 s ) D. ( 50 s ) | 11 |

4 | A man running on a horizontal road at ( 8 k m p h ) find that rain is falling vertically. He increases the speed to ( 12 k m p h ) and find the drops make an angle ( 30^{circ} ) with the vertical A. The speed of rain is ( 8 sqrt{3} k m p h ) B. The speed of rain is ( 8 sqrt{112} k m p h ) c. speed of rain wrt man is ( 8 k m p h ) D. Speed of rain wrt man is ( 8 sqrt{3} k m p h ) | 11 |

5 | подоtапу. 9. A particle is moving in a circle of radius R with constant speed. The time period of the particle is T = 1. In a time t = T/6, if the difference between average speed and average velocity of the particle is 2 ms’, find the radius R of the circle (in meters). | 11 |

6 | A particle is moving in a horizontal circle with constant speed. It has constant A. Velocity B. Acceleration c. Kinetic energy D. Displacement | 11 |

7 | A plank fitted with a gun is moving on a horizontal surface with speed of ( 4 mathrm{m} / mathrm{s} ) along the positive x-axis. The z-axis is in vertically upward direction. The mass of the plank including the mass of the mass of the gun is 50 kg. When the plank reaches the origin, a shell of mass ( 10 mathrm{kg} ) is fired at an angle of ( 60^{circ} ) with the positive x-axis with a speed of ( mathbf{v}=20 mathrm{m} / mathrm{s} ) with respect to the gun ( mathrm{n} mathbf{x}-mathrm{z} ) plane. Find the position vector of the shell at ( t=2 ) s after firing it. Take ( g= ) ( 9.8 m / s^{2} ) A. ( [15 hat{i}-24 hat{k}] m ) в. ( [28 hat{i}+15 hat{k}] m ) c. ( [15 hat{i}-18 hat{k}] m ) D. ( [14 hat{i}-15 hat{k}] m ) | 11 |

8 | 2. The time after which they are closest to each other a. 1/3 s b. 8/3 s c. 1/5 s d. 8/5 s | 11 |

9 | A vertical wall of height ( a ) running from south to north has the height. A policeman of height ( b>a ) is standing in front of the wall at a distance ( c ) from it on the eastern side. What should be the maximum distance of a crawling theif from the wall so that the thief can hide from the view of the policeman if the thief is on the other side of the wall in the west of the policeman? A ( cdot frac{a c}{b-a} ) в. ( frac{b c}{b-a} ) c. ( frac{a+b}{b-a} cdot c ) D. ( frac{a c}{a+b} ) | 11 |

10 | A vector having magnitude 30 unit makes equal angles with each of ( boldsymbol{x}, boldsymbol{y} ) and ( z ) axes. The component along each of ( x, y ) and ( z ) -axis are A ( cdot 10 sqrt{3} ) is в. ( 20 sqrt{3} ) c. ( 30 sqrt{3} ) is D. ( 18 sqrt{3} ) | 11 |

11 | 15. The horizontal range of particle is 3 u* sin 20 (0) “”sin 26 4 g (b) usin 20 (1+ + (a) u? sin 20 (2++) 2g | 11 |

12 | A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows A. its velocity is constant B. its K.E. is constant c. its acceleration is constant D. it moves in a straight line | 11 |

13 | Two forces acting in opposite directions have a resultant of ( 10 mathrm{N} 10 mathrm{N} ). What are the magnitudes of the two forces? ( mathbf{A} cdot F_{1}=40 N, F_{2}=30 N ) B. ( F_{1}=30 N, F_{2}=40 N ) C . ( F_{1}=50 N, F_{2}=40 N ) D. ( F_{1}=100 N, F_{2}=60 N ) | 11 |

14 | The position vector of a particle is ( r= ) ( a sin omega t hat{i}+a cos omega t hat{j} ) The velocity of the particle is A. Parallel to position vector B. Perpendicular to position vector c. Directed towards origin D. Directed away from the origin | 11 |

15 | A boy playing on the roof of a ( 10 mathrm{m} ) high building throws a ball with a speed of ( 10 m s^{-1} ) at an angle of ( 30^{circ} ) with the horizontal. How far from the throwing point with the ball be at the height of 10 ( mathrm{m} ) from the ground? ( (boldsymbol{g}= ) ( 10 m s^{-2}, sin 30^{circ}=1 / 2, cos 30^{circ}= ) | 11 |

16 | In the arrangement shown in the figure, the ends ( P ) and ( Q ) of an un-stretchable string move downwards with uniform speed ( U ). Pulleys ( A ) and ( B ) are fixed. The mass ( M ) moves upwards with a speed: ( mathbf{A} cdot 2 U cos theta ) B. ( frac{U}{cos theta} ) c. ( frac{2 U}{cos theta} ) ( D . U cos theta ) | 11 |

17 | A vector of magnitude 100 units is inclined at ( 30^{0} ) to another vector of magnitude 80 units. Then vector product is: A. 4000 B. ( 4000 sqrt{3} ) c. 8000 D. ( 8000 sqrt{3} ) | 11 |

18 | C. lall (14) 23. A shot is fired from a point at a distance of 200 m from the foot of a tower 100 m high so that it just passes over it horizontally. The direction of shot with horizontal is a. 30° b. 45° c. 60° d. 70° ……. 1: | 11 |

19 | A block is suspended by an ideal spring of force constant k. If the block is pulled down by applying a constant force ( F ) and if maximum displacement of the block from its initial position of rest is ( delta, ) then A ( cdot frac{F}{k}frac{2 F}{k} ) B . ( delta frac{2 F}{k} ) c. work done by force F is equal to ( F delta ) D. Increase in energy stored in the spring is ( frac{1}{2} k delta^{2} ) | 11 |

20 | A horizontal wind is blowing with a velocity ( v ) towards north-east. A man starts running towards north with acceleration ( a ). The time after which man will feel the wind blowing towards east is A ( cdot frac{v}{a} ) B. ( frac{sqrt{2} v}{a} ) c. ( frac{v}{sqrt{2} a} ) D. ( frac{2 v}{a} ) | 11 |

21 | T y m 00 -12. 9 IV Illustration 3.10 A person in a wheelchair is moving up a ramp at constant speed. Their total weight is 900 N. The ramp makes an angle of 37° with the horizontal. Calculate the component of its weight parallel and perpendicular to the ramp. 370 Fig. 3.26 | 11 |

22 | Rain is falling vertically with a speed of ( 30 mathrm{m} s^{-1} . ) A woman rides a bicycle with a speed of ( 10 mathrm{m} s^{-1} ) in the north to south direction. What is the direction in which she should hold her umbrella? | 11 |

23 | On applying brakes the angular velocity of a flywheel reduces from 900 cycles/min to 720 cycles/min in 6 seconds. Its angular retardation in rad ( / s^{2} ) will be? A . ( pi / 3 ) в. ( pi ) c. ( 2 pi / 3 ) D. ( 2 pi ) | 11 |

24 | In going from one city to another, a car travels ( 75 k m ) north, ( 60 k m ) north-west and ( 20 k m ) east. The magnitude of displacement between the two cities is (take ( sqrt{mathbf{2}}=mathbf{0 . 7}) ) A. ( 170 k m ) в. ( 137 k m ) c. ( 119 k m ) D. ( 140 k m ) | 11 |

25 | Point ( ^{prime} A^{prime} ) moves uniformly with speed ( v_{1}(=20 m / text {sec}) ) so that vector ( vec{v}_{1} ) is continuously ‘aimed’ at point ‘ ( B^{prime} ) which in turn moves rectilinearly and uniformly with velocity ( v_{2}(=10 m / s e c) ) along the path ( P rightarrow Q ) as shown in the figure. If the time (in sec)when the points ( A ) and ( B ) converge is ( frac{3 k}{7} . ) Then find the value of ( k ? ) | 11 |

26 | In a uniform circular motion, the magnitude and direction of velocity at different points remain the same. A. True B. False | 11 |

27 | 3. Cannon A is located on a plain a distance L from a wall of height H. On top of this wall is an identical cannon (cannon B). Ignore air resistance throughout this problem. KL- Fig. 5.185 Also ignore the size of the cannons relative to L and H. The two groups of gunners aim the cannons directly at each other. They fire at each other simultaneously, with equal muzzle speed Vo. What is the value of v, for which the two cannon balls collide just as they hit the ground? | 11 |

28 | A particle moves along a circle of radius ( 2 m ) with a constant speed of ( 8 m / s . ) It covers the quarter of circle in sec? A ( cdot frac{pi}{16} ) в. ( c cdot frac{pi}{4} ) D. | 11 |

29 | 1. Two forces, each of magnitude F have a resultant of the same magnitude F. The angle between the two forces is (a) 45° (b) 120° (c) 150° (d) 60° 1. 10 | 11 |

30 | In reaching her destination, a backpacker walks with an average velocity of ( 1 m / s, ) due west. This average velocity results, because she hikes for ( 6 k m ) with an average velocity of ( 3 m / s ) due west, turns around, and hikes with an average velocity of ( 0.3 m / s ) due east.How far to east did she walk (in kilometers)? A. 1.714 в. 2 ( c .6 ) D | 11 |

31 | An uniform circular motion is an uniform velocity motion A. True B. False | 11 |

32 | A wheel rotating at 12 rev/s is brought to rest in ( 6 s . ) The average angular deceleration in ( r a d / s^{2} ) of the wheel during this process is? A . ( 4 pi ) в. 4 ( c cdot 72 ) D. ( frac{1}{pi} ) ( E . pi ) | 11 |

33 | 8. A particle is projected up an inclined plane of inclination B at an elevation a to the horizontal. Find the ratio between tan a and tan B, if the particle strikes the plane horizontally. | 11 |

34 | Two tall buildings are ( 80 m ) apart. The velocity with which a ball should be thrown horizontally from a window ( 95 m ) above the ground in one building so that it will enter a window 15 m above the ground in the second building is : ( (g= ) ( left.10 m / s^{2}right) ) A. ( 15 mathrm{m} / mathrm{s} ) B. ( 5 m / s ) c. ( 10 mathrm{m} / mathrm{s} ) D. 20 ( m / s ) | 11 |

35 | Illustration 5.55 A man is coming down an incline of angle 30°. When he walks with speed 2/3 ms’ he has to keep his umbrella vertical to protect himself from rain. The actua speed of rain is 5 ms. At what angle with vertical should he keep his umbrella when he is at rest so that he does not get drenched? 30° Fig. 5.109 | 11 |

36 | 45. In a two-dimensional motion of a particle, the particle moves from point A, with position y vector , to point B, with po- sition vector 72. If the magnitudes of these vectors are, respectively, r = 3 and r2 = 4 and the angles they make with the x-axis are 0, =75° and e2 =15°, respectively, then find the magnitude of the Fig. 3.80 displacement vector. a. 15 b. 813 c. 17 d. /15 We | 11 |

37 | When a body is projected from a level ground, the ratio of it’s speed in the vertical and horizontal direction is 4: 3 If the velocity of projection is ( u, ) the time after which the ratio of the velocities in the vertical and horizontal directions is reversed is A. ( frac{7 u}{20 g} ) B. ( frac{35 u}{10 g} ) c. ( frac{9 u}{g} ) D. ( frac{10 u}{g} ) | 11 |

38 | hollis projected from the ground with velocity v such that its range is maximum. Column I Column II Velocity at half of the maximum height i Velocity at the maximum height Change in its velocity when it returns to the ground tc. iv. Average velocity when it reaches the maximum height | 11 |

39 | The position of a body moving along ( x- ) axis at time ( t ) is given by ( boldsymbol{x}=left(boldsymbol{t}^{2}-boldsymbol{4} boldsymbol{t}+right. ) 6) ( m . ) The distance travelled by body in time interval ( t=0 ) to ( t=3 ) s is ( mathbf{A} cdot 5 m ) B. ( 7 m ) c. ( 4 m ) D. ( 3 m ) | 11 |

40 | Ay 1. Which of the following statements is/are correct (Fig. 3.81)? a. The sign of the x-component of d, is positive and that of d2 is negative. b. The signs of the y-com- ponents of d, and d2 are Fig. 3.81 positive and negative, re- spectively. c. The signs of the x- and y-components of d. + d, are positive. d. None of these. | 11 |

41 | All straight wires are very long. Both ( boldsymbol{A B} ) and ( C D ) are arcs of the same circle, both subtending right angles at the centre ( O . ) Then the magnetic field at 0 is- A ( cdot frac{mu text { is }}{4 pi R R R} ) B・ ( frac{mu_{text {Di }}}{4 pi} sqrt{2} ) c. ( frac{mu text { li }}{2 pi R_{R}} ) D. ( frac{mu_{0} i}{2 pi R}(pi+1) ) | 11 |

42 | Fill in the blanks. At any point in a circular motion the direction of linear velocity of the particle is | 11 |

43 | 39. Two forces Ē = 500 N due east and F = 250 N due north have their common initial point. F2 – F is a. 250 V5 N, tan-‘(2) W of N b. 250 N, tan-|(2) W of N c. Zero d. 750 N, tan-‘(3/4) N of W | 11 |

44 | For given vectors, ( vec{a}=2 hat{i}-hat{j}+2 hat{k} ) and ( vec{b}=-hat{i}+hat{j}-hat{k}, ) find the unit vector in the direction of the vector ( vec{a}+vec{b} ) | 11 |

45 | A projectile is thrown into space so as to have the maximum possible horizontal range equal to ( 400 m ). Taking the point of projection as the origin, the coordinates of the point where the velocity of the projectile is minimum are: ( mathbf{A} cdot(400,100) ) в. (200,100) c. (400,200) D. (200,200) | 11 |

46 | 22. A spy plane is being tracked by a radar. Att=0, its position is reported as (100 m, 200 m, 1000 m). 130 s later, its position is reported to be (2500 m, 1200 m, 1000 m). Find a unit vector in the direction of plane velocity and the magnitude of its average velocity. | 11 |

47 | An ice cream truck travels around many circular curves at constant speeds. Each table represents the speed of the truck and radii for some of these curves During which curve is the magnitude of the truck’s acceleration the greatest?? A. Radius of curve – Speed of Truck, ( 30 mathrm{m}-5 mathrm{m} / mathrm{s} ) B. Radius of curve – Speed of Truck, ( 60 mathrm{m}-10 mathrm{m} / mathrm{s} ) c. Radius of curve – Speed of Truck, ( 90 mathrm{m}-15 mathrm{m} / mathrm{s} ) D. Radius of curve – speed of Truck, ( 120 mathrm{m}-20 mathrm{m} / mathrm{s} ) E. The magnitude of the acceleration for the ice cream truck on all these curves is the same | 11 |

48 | A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the ratio ( frac{mid text {displacement} mid}{text {distance}} ) is ( mathbf{A} cdot mathbf{0} ) B. ( c cdot frac{2}{7} ) D. ( frac{7}{11} ) | 11 |

49 | A bomb is dropped from a flying aeroplane. Its path will be A. an arc of a circle B. a parabola c. a zig-zag path D. a straight vertical path in the do rection | 11 |

50 | In a projectile motion from a point of horizontal surface to another point on the same surface (Take ( overrightarrow{boldsymbol{a}}= ) acceleration and ( vec{v}= ) instantaneous velocity) This question has multiple correct options A. ( vec{a} cdot vec{v}=0 ) at maximum height B . ( vec{a} cdot vec{v}=0 ) only if angle of projection is ( 90^{circ} ) c. ( vec{a} times vec{v}= ) constant every where in air D. None of these | 11 |

51 | If ( vec{p} & vec{s} ) are not perpendicular to each other and ( vec{r} times vec{p}=vec{q} times vec{p} & vec{r} . vec{s}=0 ) ( operatorname{then} vec{r}= ) A ( cdot vec{p} . vec{s} ) В ( cdot vec{q}+left(frac{vec{q} . vec{s}}{vec{p} . vec{s}}right) vec{p} ) c. ( vec{q}-left(frac{vec{q} . vec{s}}{vec{p} . vec{s}}right) vec{p} ) D. ( vec{q}+mu vec{p} ) for all scalars ( mu ) | 11 |

52 | A boats man finds that he can save 6 ( sec ) in crossing a river by quicker path, then by shortest path if the velocity of boat and river be respectively ( 17 mathrm{m} / mathrm{s} ) and ( 8 mathrm{m} / mathrm{s} ), then river width is? ( mathbf{A} cdot 675 mathrm{m} ) B. ( 765 mathrm{m} ) ( c .567 mathrm{m} ) D. 657 m | 11 |

53 | U 2.11 . J NIC . 1.J110 41. A ball rolls off the top of a staircase with a horizontal velocity u ms. If the steps are h metre high and b metre wide, the ball will hit the edge of the nth step, if 2 2hu 2hu² a. n= b. n= gb 862 d. n= c. n=2hu? 8b2 . n. hu2 | 11 |

54 | A body moves in a plane so that the displacements along the ( x ) and ( y ) axes are given by ( boldsymbol{x}=mathbf{3} boldsymbol{t}^{3} ) and ( boldsymbol{y}=mathbf{4} boldsymbol{t}^{3} . ) The velocity of the body is : A ( .10 t ) B . 15 ( c cdot 15 t^{2} ) D. ( 25 t^{2} ) | 11 |

55 | Given that ( vec{A} ) and ( vec{B} ) are greater than one, then the magnitude of ( (vec{A} times vec{B}) ) can not be A . equal to ( overrightarrow{A B} ) B. less than ( vec{B} ) c. more than ( |vec{A}||vec{B}| ) D. equal to ( vec{A} / vec{B} ) | 11 |

56 | Ship A is located ( 4 k m ) north and ( 3 k m ) east of ship B. Ship A has a velocity of ( 20 mathrm{kmh}^{-1} ) towards the south and ship ( mathrm{E} ) is moving at ( 40 mathrm{kmh}^{-1} ) in a direction ( 37^{circ} ) north of east. ( X ) and ( Y ) axes are along east and north directions, respectively. This question has multiple correct options A. Velocity of A relative to B is ( -32 hat{i}-44 hat{j} ) B. Position of A relative to B as a function of time is given by ( vec{r}_{A B}=(3-32 t) hat{i}+(4-44 t) hat{j} ) c. Velocity of A relative to B is ( 32 hat{i}-44 hat{j} ) D. Position of A relative to B as a function of time is given by ( (32 t hat{i}-44 t hat{j}) ) | 11 |

57 | 10. A sail boat sails 2 km due east, 5 km 37° south of east, and finally an unknown displacement. If the final displacement of the boat from the starting point is 6 km due east, determine the third displacement. | 11 |

58 | At the maximum height of a projectile, the velocity and acceleration are A. parallel to each other B. antiparallel to each other c. perpendicular to each other D. inclined to each other at ( 45^{circ} ) | 11 |

59 | You throw a ball which a launch velocity of ( overrightarrow{boldsymbol{v}}=(mathbf{3} hat{boldsymbol{i}}+mathbf{4} hat{boldsymbol{j}}) boldsymbol{m} / boldsymbol{s} ) the maximum height attaind by the body is? A. ( 0.8 m ) в. ( 0.2 m ) ( mathrm{c} .2 .3 mathrm{m} ) D. ( 5.3 mathrm{m} ) | 11 |

60 | 29 Two tall buildings are 30 m apart. The speed with which a ball must be thrown horizontally from a window 150 m above the ground in one building so that it enters a window 27.5 m from the ground in the other building is a. 2 ms-1 b. 6 ms c. 4 ms 1 d. 8 ms-1 | 11 |

61 | A particle is travelling in a circular path of radius 4 m. At certain instant the particle is moving at ( 20 mathrm{m} / mathrm{s} ) and its acceleration is at an angle of ( 37^{circ} ) from the direction to the centre of the circle as seen from the particle. (i) At what rate is the speed of the particle increasing? (ii) What is the magnitude of the acceleration? | 11 |

62 | Find the average velocity of a projectile between the instants it crosses half the maximum height. It is projected with a speed ( u ) at an angle ( theta ) with the horizontal. | 11 |

63 | A particle is moving around a circular path with uniform angular speed ( ( omega ) ) The radius of the circular path is ( (r) ) The acceleration of the particle is: A ( cdot frac{omega^{2}}{r} ) в. ( frac{omega}{r} ) c. ( v ) D. ( v r ) | 11 |

64 | 10. 10. A particle is projected with a velocity v such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where g is acceleration due to gravity) | 11 |

65 | Wind is blowing from west to east along two parallel tracks. A train is moving on each track in opposite directions. They have same speed when no wind is blowing. Now, one train has speed double that of the other. The speed of each train is A. Equal to that of wind B. Double that of wind c. Three times that of wind D. Half of that of wind | 11 |

66 | a. TUJU ody is projected at an angle of 30° with the horizontal od with a speed of 30 ms. What is the angle horizontal after 1.5 s? (g = 10 ms-2) 200 b. 30° c. 60° d. 900 | 11 |

67 | A wheel, starting from rest, rotates with a uniform angular acceleration of 2rads ( ^{-2} ). The number of rotations it performs in the tenth second is ( A cdot 3 ) B. 6 ( c cdot 9 ) D. 12 | 11 |

68 | A large rectangular box falls vertically with an acceleration a. A toy gun fixed at ( A ) and aimed towards 0 fires a particle P. Which of the following is false A. P will hit ( mathrm{C} ) if ( mathrm{a}=mathrm{g} ) B. P will hit the roof BC if a ( >g ) c. P will hit the wall cD if ( a<g ) D. may be either ( (a),(b) ) or (c), depending on the projection speed of | 11 |

69 | Consider an expanding sphere of instantaneous radius ( R ) whose total mass remains constant. The expansion is such that the instantaneous density ( rho ) remains uniform throughout the volume. The rate of fractional change in density ( left(frac{1}{rho} frac{d p}{d t}right) ) is constant. The velocity ( v ) of any point on the surface of the expanding sphere is proportional to A ( cdot R^{2 / 3} ) в. ( R ) c. ( R^{3} ) D. ( frac{1}{R} ) | 11 |

70 | A particle is moving along a circular path of radius ( 5 m ) with a uniform speed ( 5 m s^{-1} . ) What is the magnitude of average acceleration during the interval in which particle completes half revolution? | 11 |

71 | L. V SM 70 18. A particle is projected with a velocity v so that its on a horizontal plane is twice the greatest height att If g is acceleration due to gravity, then its range is 4,2 h 4v 5g- | 11 |

72 | The circular motion of a particle with constant speed is A. periodic and simple harmonic B. simple harmonic but not periodic. c. neither periodic nor simple harmonic. D. periodic but not simple harmonic. | 11 |

73 | A particle moves along a straight line such that its displacement at any time is given by ( s=left(t^{3}-6 t^{2}+3 t+4right) m ) Find the velocity when the acceleration is zero. | 11 |

74 | A ball is thrown upwards. It returns to ground describing a parabolic path.Which of the following remains constant. A. Speed of the ball B. Kinetic energy of the ball c. vertical component of velocity D. Horizontal component of velocity | 11 |

75 | Consider the following two statements A and B and identify the correct option: A) When a rigid body is rotating about its own axis at a given instant, all particles of body possess same angular velocity B) When a rigid body is rotating about its own axis, the linear velocity of a particle is directly proportional to its perpendicular distance from axis. A . A is true but B is false B. A is false but B is true c. Both A and B are true D. Both A and B are false | 11 |

76 | A circular disc is rotating about its own axis at constant angular acceleration. If its angular velocity increases from 210 rpm to 420 rpm during 21 rotations then the angular acceleration of disc is : A. ( 5.5 mathrm{rad} / mathrm{s}^{2} ) B. 11 rad / ( s^{2} ) c. ( 16.5 mathrm{rad} / mathrm{s}^{2} ) D. 22 rad / ( s^{2} ) | 11 |

77 | Illustration 4.3 A particle moves from position A to position B in a path as shown in Fig 4.5. If the position vectors , and i, making an angle between them are given, find the magnitude of displacement. Fig. 4.5 | 11 |

78 | A wheel has angular acceleration of ( 3.0 mathrm{rad} / mathrm{s}^{2} ) and an intial angular speed of 2.00 rad/s. In a time of ( 2 s ) it has rotated through an angle (in radians) of ( mathbf{A} cdot mathbf{6} ) B. 10 c. 12 D. | 11 |

79 | U. Noe u ulls 37. A platform is moving upwards with an acceleration of 5 ms. At the moment when its velocity is u=3 ms, a ball is thrown from it with a speed of 30 ms w.r.l. platform at an angle of O= 30° with horizontal. The time taken by the ball to return to the platform is a. 2s b. 3. c. 15 d. 2.5s us 1 | 11 |

80 | Associate law of vector addition is A. The sum of vectors remains same irrespective of their order or grouping in which they are arranged. B. The sum of vectors is different irrespective of their order or grouping in which they are arranged. C. The sum of vectors changes with the change of their order or grouping in which they are arranged D. None of the above | 11 |

81 | When a man is standing, rain drops appear to him falling at ( 60^{circ} ) from the horizontal from his front side. When he is travelling at ( 5 k m / h ) on a horizontal road they appear to him falling at ( 30^{circ} ) from the horizontal from his front side. The actual speed of the rain is ( ( ) in ( boldsymbol{k m} / boldsymbol{h}) ) A . 3 B. 4 c. 5 D. 6 | 11 |

82 | 6. Five equal forces of 10 N each are applied at one point and all are lying in one plane. If the angles between them are equal, the resultant force will be (a) Zero (b) 10 N (c) 20 N (d) 10/2N | 11 |

83 | An astronaut, orbiting in a spaceship round the earth, has a centripetal acceleration of ( 6.67 m / s^{2} . ) Find the height of the spaceship above the surface of the earth. ( left(G=6.67 times 10^{11} N m^{2} / k g^{2}, ) radius of right. the earth ( =6400 mathrm{km} ) | 11 |

84 | u ULUIT OLICI, ull wey Will Conde. Illustration 5.62 Two particles A and B are moving with constant velocities y, and vs. At t=0, v, makes an angle 8 with the line joining A and B and v, makes an angle e2 with the line joining A and B. 10, Fig. 5.127 a. Find the condition for A and B to collide. b. Find the time after which A and B will collide if separation between them is dat t = 0 | 11 |

85 | State whether the given statement is True or False : The earth moves around the sun with a | 11 |

86 | 22. In the above problem, what is the angle of projection was horizontal? a. tan-(1/4). b. tan-‘(4/3) c. tan-+(3/4) d. tan-(1/2) | 11 |

87 | From point ( A ) located on a highway, one has to get by a car as soon as possible to point ( B ) located in the field at a distance ( l ) from point ( D . ) If the car moves ( n ) times slower in the field, at what distance ( x ) from ( D ) one must turn off the highway. A ( cdot x=frac{l}{sqrt{n^{3}-1}} ) B. ( x=frac{l}{sqrt{n^{2}-1}} ) c. ( _{x}=frac{l}{sqrt{n^{3}-2}} ) D. ( x=frac{l}{sqrt{n^{2}-2}} ) | 11 |

88 | Position vector of a particle is given by ( vec{r}=a cos omega t hat{i}+a sin omega t hat{j} . ) Which of the following is/are true? This question has multiple correct options A. velocity vector is parallel to position vector B. velocity vector is perpendicular to position vector c. acceleration vector is directed towards the origin D. acceleration vector is directed away from the origin | 11 |

89 | Q Type your question a wall. The jeep has to take a sharp perpendicular turn along the wall. A rocket flying at uniform speed of 100kmh ( ^{-1} ) starts from the wall towards the jeep which is ( 30 k m ) away. The rocket reaches the windscreen and returns to wall. Total distance covered by the rocket is A . ( 100 k m ) ( mathbf{B} .50 k m ) ( c .37 k m ) D. ( 75 k ) | 11 |

90 | A particle is projected with a velocity making an angle ( theta ) with the horizontal. What is the radius of curvature of the parabola where the particle makes an angle ( theta ) /2 with the horizontal? | 11 |

91 | A block is moving in a circular path at constant speed. Which of the following statements is/are true? I. The velocity is constant. II. The direction of motion is constant. III. The magnitude of velocity is constant. A. II only B. I and III only c. ॥ and III only D. I and II only E. III only | 11 |

92 | An object ( A ) is kept fixed at the point ( x=3 m ) and ( y=1.25 m ) on a plank ( P ) raised above the ground. At time ( t= ) the plank starts moving along the positive ( x ) -direction with an acceleration ( 1.5 m / s^{2} . ) At the same instant a stone is projected from the origin with a velocity ( vec{u} ) as shown in the figure. A stationary person on the ground observes the stone hitting the object during which it makes a downwards motion at the angle of ( 45^{circ} ) to the horizontal. All the motions are in ( x ) -y plane. Find ( vec{u} ) and the time after which the stone hits the object (Take ( boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2} mathbf{)} ) | 11 |

93 | Consider the motion of a particle described by ( x=a cos t, y=a sin t ) and ( z=t . ) The trajectory traced by the particle as a function of time is A. Helix B. Circular c. Elliptical D. Straight line | 11 |

94 | Three bodies are projected in three different ways: a) vertically up b) vertically down c) horizontally, with same speed from top of a tower. The time taken by the bodies to reach the ground in increasing order would be: ( mathbf{A} cdot t_{b}<t_{a}<t_{c} ) в. ( t_{c}<t_{a}<t_{b} ) c. ( t_{b}<t_{c}<t_{a} ) D ( cdot t_{a}<t_{b}<t_{c} ) | 11 |

95 | Resultant of two vectors ( vec{P} ) and ( vec{Q} ) is inclined at ( 45^{circ} ) to either of them. What is the magnitude of the resultant? ( mathbf{A} cdot sqrt{P^{2}+Q^{2}} ) B . ( sqrt{P^{2}-Q^{2}} ) ( c cdot P+Q ) D. ( P-Q ) | 11 |

96 | A particle is projected up with an initial velocity of 80 the ball will be at a height of 96 from the ground after | 11 |

97 | A body moving in circular motion with constant speed has: A. constant velocity B. constant acceleration c. constant kinetic energy D. constant displacement | 11 |

98 | Example 5.7 A moves with constant velocity u along then x-axis. B always has velocity towards A. After how much time will B meet A if B moves with constant speed V? What distance will be travelled by A and B? JAU Fig. 5.183 | 11 |

99 | A person standing near the edge of the top of a building throws two balls ( A ) and B. The ball ( A ) is thrown vertically upward and ( B ) is thrown vertically downward with the same speed. The ball ( A ) hits the ground with a speed ( v_{A} ) and the ball ( B ) hits the ground with a speed ( boldsymbol{v}_{B} . ) We have: В . ( v_{A}<v_{B} ) c. ( v_{A}=v_{B} ) D. the relation between ( v_{a} ) and ( v_{b} ) depends on height of the building above the ground | 11 |

100 | Propeller blades in aeroplane are ( 2 mathrm{m} ) long. When propeller is rotating at 1800 rev/min, compute the tangential velocity of tip of the blade. | 11 |

101 | 6. The speed of rain with respect to the moving man is a. 0.5 ms b. 1.0 ms? c. 0.5 13 ms -1 d. 0.45 ms-1 | 11 |

102 | Illustration 3.22 A bird moves with velocity 20 ms in a direction making an angle of 60° with the eastern line and 60° with vertical upward. Represent the velocity vector in rectangular form. | 11 |

103 | Uniform linear motion is a/an motion while uniform circular motion is a/an motion. A . accelerated, non accelerated B. non accelerated, accelerated c. deviated, retarded D. uniform, retarded | 11 |

104 | 9. The time taken for the displacement vectors of two bodies to be come perpendicular to each other is a. 0.1s b. 0.2 s c. 0.8 s d. 0.6 s | 11 |

105 | A particle of mass ( 1 mathrm{gm} ) and charge ( 1 mu C ) is held at rest on a frictionless horizontal surface at distance ( 1 mathrm{m} ) from the fixed charge 2 mC. If the particle is released, it will be repelled. The speed of the particle when it is at a distance of ( 10 mathrm{m} ) from the fixed charge A ( cdot 60 m s^{-1} ) B. ( 100 mathrm{ms}^{-1} ) c. ( 90 m s^{-1} ) D. ( 180 mathrm{ms}^{-1} ) | 11 |

106 | The resultant of two forces which are equal in magnitude is equal to either of two vectors in magnitude. Find the angle between the forces. A .60 B . 45 ( c cdot 90 ) D. ( 120^{circ} ) | 11 |

107 | An object is thrown between two tall buildings ( 180 mathrm{m} ) from each other. The object thrown horizontally from a window ( 55 mathrm{m} ) above the ground from one building strikes a window ( 10 mathrm{m} ) above the tom ground in another building. Find out the speed of projection. A. 60 B. 80 ( c .70 ) D. 90 | 11 |

108 | A particle of mass ( mathrm{m} ) is moving in a circular path of constant radius r such that its centripetal acceleration ( a_{c} ) is varying with time ( t ) as ( a_{c}=k^{2} r t^{2} ) where ( k ) is a constant. The power delivered to the particle by the forces acting on it, is? A. zero B. ( m k^{2} r^{2} t^{2} ) ( mathbf{c} cdot m k^{2} r^{2} t ) ( mathbf{D} cdot m k^{2} r t ) | 11 |

109 | 3. Statement I: If the string of an oscillating simple pendulum is cut, when the bob is at the mean position, the bob falls along a parabolic path. Statement II: The bob possesses horizontal velocity at the mean position. | 11 |

110 | 9. A stone is projected from the ground with velocity 50 m at an angle of 30°. It crosses a wall after 3 sec. How far beyond the wall the stone will strike the ground (g = 10 m/sec)? (a) 90.2 m (b) 89.6 m (c) 86.6 m (d) 70.2 m 10 portiola in woh that its range | 11 |

111 | 2. 00 0. 00 * 15. If the helicopter flies at constant velocity, find the x y coordinates of the location of the helicopter when the package lands. a. 160 m, 320 m b. 100 m, 200 m c. 200 m, 400 m d. 50 m, 100 m | 11 |

112 | A particle moves with constant speed ( v ) along a regular hexagon ABCDEF in the same order. Then the magnitude of the velocity for its motion from A to This question has multiple correct options ( mathbf{A} cdot_{F} ) is ( frac{v}{5} ) B ( cdot ) D is ( frac{v}{3} ) c. ( quad mathrm{c} ) is ( frac{v sqrt{3}}{2} ) D. B is ( v ) | 11 |

113 | 6. A particle is moving in xy-plane with y = x/2 and v=4-2t. Choose the correct options. a. Initial velocities in x and y directions are negative b. Initial velocities in x and y directions are positive c. Motion is first retarded, then accelerated. d. Motion is first accelerated, then retarded. | 11 |

114 | If the length of second’s hand of a clock is ( 10 mathrm{cm}, ) the speed of its tip ( left(text { in } mathrm{cm} mathrm{s}^{-1}right) ) is nearly ( A cdot 2 ) в. 0.5 c. 1.5 D. | 11 |

115 | Illustration 5.45 stion 5.45 A man can swim at the rate of 5 kmh in ater. A 1-km wide river flows at the rate of 3 kmh. e man wishes to swim across the river directly opposite to the starting point. Along what direction must the man swim? b. What should be his resultant velocity? How much time will he take to cross the river? | 11 |

116 | Illustration 3.4 Two forces whose magnitudes are in the ratio 3: 5 give a resultant of 28 N. If the angle of their inclination is 60°, find the magnitude of each force. | 11 |

117 | A particle of mass ( 5 g ) is moving in a circle of radius ( 0.5 m ) with an angular velocity of 6 rad( / )s. Find (i) the change in linear momentum in half a revolution (ii) the magnitude of the acceleration of the particle. | 11 |

118 | JUL, 2011) 2. Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30° and 60° with respect to the horizontal respectively as shown in the figure. The speed of A is 1003 ms. At time t = 0 s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If a t = to, A just escapes being hit by B, to in seconds is 130° 60° Fig. A.55 (JEE Advanced, 2014) | 11 |

119 | Illustration 3.27 A bob of weight 3 N is in equilibrium under the action of two strings 1 and 2 (Fig. 3.52). Find the tension forces in the strings. LLLLLLL 30.12 ITTI7777 3N Fig. 3.52 | 11 |

120 | Three force ( overrightarrow{boldsymbol{p}}, overrightarrow{boldsymbol{Q}} ) and ( quad overrightarrow{boldsymbol{R}} ) acting with TA,IB,IC where I is the incentance of ( triangle A B C ) are in equim ( vec{P}_{Q}, quad_{R} ) is | 11 |

121 | the two balls will collide at time ( t= ) ( A cdot 2 s ) В. 5 s ( c .10 s ) ( 0.3 s ) | 11 |

122 | How long does it stay in the air (in s)? A . 37 в. 37.1 ( c .36 ) D. 35 5 | 11 |

123 | A ball is moving uniformly in a circular path of radius ( 1 m ) with a time period of 1.5 ( s ). If the ball is suddenly stopped at ( t=8.3 s, ) the magnitude of the displacement of the ball with respect to its position at ( t=0 s ) is closest to: ( mathbf{A} cdot 1 m ) в. 33 т ( c .3 m ) D. ( 2 m ) | 11 |

124 | For the displacement-time graph shown in the figure above, find the velocity at point ( mathbf{A} ) A. ( 4 mathrm{m} mathrm{s}^{-1} ) B. 3 ( mathrm{m} ) s ( ^{-1} ) ( c cdot 5 m s^{-} ) D. ( 6 mathrm{m} ) s ( ^{-1} ) | 11 |

125 | Ring of radius ( R ) rotating about axis of ring such that angular velocity is given as omega ( =5 t . ) Find acceleration of a point ( boldsymbol{P} ) on rim after ( mathbf{5} ) sec? ( mathbf{A} cdot 5 R ) в. 25 В c. ( sqrt{650} R ) D. None of these | 11 |

126 | A merry go round has a radius of ( 4 m ) and completes a revolution in 2 s. Then acceleration of a point on its rim will be: ( mathbf{A} cdot 4 pi^{2} ) В . ( 2 pi^{2} ) ( mathbf{c} cdot pi^{2} ) D. zero | 11 |

127 | If a boat can travel with a speed of ( v ) in still water, which of the following trips will take the least amount of time? A. travelling a distance of ( 2 d ) in still water. B. travelling a distance of ( 2 d ) across (perpendicular to) the current w.r.t. in a stream C. travelling a distance ( d ) downstream and returning a distance ( d ) upstream D. travelling a distance ( d ) upstream and returning a distance ( d ) downstream | 11 |

128 | The distance between the point ( P(x, y, z) ) and plane ( x z ) is : A . ( x ) B. ( y ) ( c ) D. ( x y ) | 11 |

129 | A policeman on duty detects a drop of ( 10 % ) in the pitch of the horn of a moving car as it crosses him. If the velocity of sound is ( 330 m / s, ) the speed of the car will be ( mathbf{A} cdot 36.7 m / )sec в. ( 17.3 mathrm{m} / mathrm{sec} ) ( mathbf{c} .25 mathrm{m} / mathrm{sec} ) D. ( 27 mathrm{m} / mathrm{sec} ) | 11 |

130 | In the absence of air resistance, a ball thrown horizontally from a tower with velocity v, will land after time T seconds. If, however, air resistance is taken into account, which statement is correct? A. The ball lands with a horizontal velocity less than v after more than T seconds B. The ball lands with a horizontal velocity less than v after T seconds c. The ball lands with a horizontal velocity v after more than ( T ) seconds D. The ball lands with a horizontal velocity v after seconds | 11 |

131 | Assertion In circular motion work done by all the forces acting on the body is zero. Reason Centripetal force and velocity are | 11 |

132 | ( sum_{k}^{i} ) | 11 |

133 | U sllele on IS POSiuve. 8. A small ball is projected along the surface of a smooth inclined plane with speed 10 ms’ along the direction shown at t = 0. The point of projection is origin, z-axis is along vertical. The acceleration due to gravity is 10 ms? Az-axis 10, 379 x-axis Fig. A.41 Column I lists the values of certain parameters related to motion of ball and Column II lists different time instants. Match appropriately. Column I Column II i. Distance from x-axis is a. 0,5 s 2.25 m Speed is minimum b. 1.0 s iii. Velocity makes angle c. 1.5 s 37° with x-axis d. 2.0s | 11 |

134 | Illustration 3.23 A particle is initially at point A(2, 4, 6) m moves finally to the point B(3, 2, -3) m. Write the initial position vector, final position vector, and displacement vector of the particle. | 11 |

135 | In the given figure, velocity of the body at ( A ) is A. Zero B. Unity c. Maximum D. Infinite | 11 |

136 | Illustration 5.11 Figure 5.11 shows two positions A and B at the same height h above the ground. If the maximum height of the projectile is H, then determine the time t elapsed between the positions A and B in terms of H. |(H-h) Fig. 5.11 | 11 |

137 | A body moves in a circle covers equal distance in equal intervals of time. Which of the following remains constant A. Velocity B. Acceleration c. speed D. Displacement | 11 |

138 | Starting from rest the fly wheel of a motor attains an angular velocity of ( 60 r a d / s ) in ( 5 s, ) the angular acceleration of the fly wheel is: A ( cdot 6 ) rad/s( ^{2} ) B. 12 rad / ( s^{2} ) C ( .300 mathrm{rad} / mathrm{s}^{2} ) D. 150 rad/s( ^{2} ) | 11 |

139 | Sol. When the stone is released, it moves down executing a circular motion. At any instant, the stone accelerates towards (w.r.t.) the center of its revolution 0, that is, centripetal acceleration a, and simultaneously accelerates down with an acceleration, that is, gravitational acceleration g; ā, = 0ʻr. Resolving ä, and along the tangent, we obtain the tangential acceleration of the stone as a,=g cos e. (tangent) g cos e Fig. 5.151 Angular acceleration, a=“, 8 cos e = a= (since r = 1) w do do -, we obtain @do_8 cos Putting a= 0 der = @do=(g/l) cos e do. Integrating both the sides, we obtain jo do 4 jcose do * = sine or o = V1 sin e Putting 1 = 1 m and 6 = 30°, we obtain 2(10) sin 30° -= V10 = @=3.1 rads-1 V W = | 11 |

140 | — – – – 5. All the particles thrown with same initial velocity would strike the ground. By 1, a. with same speed b. simultaneously c. time would be least for the particle thrown with velocity v downward i.e., particle 1 d. time would be maximum for the F | 11 |

141 | A jet of water is projected at an angle ( theta=45^{circ} ) with horizontal from point ( A ) which is situated at a distance ( x=O A ) ( =(a) 1 / 2 m,(b) 2 m ) from a vertical wall. If the speed of projection is ( v_{0}= ) ( sqrt{10} m s^{-1}, ) find point ( P ) of striking of the water jet with the vertical wall. | 11 |

142 | How many minimum number of coplanar vectors which represent same physical quantity having different magnitudes can be added to give zero resultant. A . (A) 2 в. (В) 3 ( c cdot(c) 4 ) D. (D) 5 | 11 |

143 | If a body is projected with certain velocity making an angle ( 30^{circ} ) with the horizontal, then A. its horizontal velocity remains constant B. its vertical velocity changes c. on falling to the ground its vertical displacement is zero D. All of the above | 11 |

144 | A car traveled the total distance of ( x ) in three equal intervals, first at a speed of ( 10 mathrm{km} / mathrm{h} . ) The second at a speed of 20 ( mathrm{km} / mathrm{h} ) and the last third at a speed of 60 km/h. Determine the average speed of the car over the entire distance ( x ) | 11 |

145 | A point moves along a circle with a velocity ( boldsymbol{v}=boldsymbol{a} boldsymbol{t}, ) where ( boldsymbol{a}=mathbf{0 . 5 0} boldsymbol{m} / boldsymbol{s}^{2} ) The total acceleration of the point at the moment when it covered the ( n^{t h}(n= ) 0.10) fraction of the circle after the beginning of motion in ( m / s^{2} ) is ( frac{x}{10} . ) Find ( mathcal{L} ) | 11 |

146 | A body of mass ( 5 k g ) under the action of constant force ( overrightarrow{boldsymbol{F}}=boldsymbol{F}_{boldsymbol{x}} hat{boldsymbol{i}}+boldsymbol{F}_{boldsymbol{y}} hat{boldsymbol{j}} ) has velocity at ( t=0 s ) as ( vec{v}=(6 hat{i}-2 hat{j}) m / s ) and ( operatorname{at} t=10 s ) as ( vec{v}=+6 hat{j} m / s . ) The force ( overrightarrow{boldsymbol{F}} ) is: A ( cdot(-3 hat{i}+4 hat{j}) N ) В ( cdotleft(-frac{3}{5} hat{i}+frac{4}{5} hat{j}right) N ) c. ( (3 hat{i}-4 hat{j}) N ) D ( cdotleft(frac{3}{5} hat{i}-frac{4}{5} hat{j}right) N ) | 11 |

147 | OABC is a current carrying square loop an electron is projected from the centre of loop along its diagonal ( A C ) as shown. Unit vector in the direction of initial acceleration will be ( A cdot hat{k} ) B. ( -left(frac{hat{i}+hat{j}}{sqrt{2}}right) ) ( c .-hat{k} ) ( frac{hat{i}+hat{j}}{sqrt{2}} ) | 11 |

148 | Hence, digIC VIWA UNU D-70 T -luv Illustration 3.6 Two forces of unequal magnitude simultaneously act on a particle making an angle e(=120°) with each other. If one of them is reversed, the acceleration of the particle is becomes 13 times. Calculate the ratio of the magnitude of the forces. | 11 |

149 | A uniform sphere of mass ( M ) and radius ( R ) is placed on a smooth horizontal ground. The angular acceleration of sphere if force ( boldsymbol{F} ) is applied on it at a distance ( 7 frac{R}{5} ) from ground level is ( ^{mathrm{A}} cdot frac{F}{2 M R} ) в. ( frac{F}{M R} ) c. ( frac{F R}{M} ) D. ( frac{2 F}{M R} ) | 11 |

150 | If a particle moves with an acceleration, then which of the following can remains constant A. Both speed and velocity B. Neither speed nor velocity c. only the velocity D. Only the speed | 11 |

151 | 14. A river flows with a speed more than the maximum spec with which a person can swim in still water. He intends to cross the river by the shortest possible path (i.e., he wants to reach the point on the opposite bank which directly opposite to the starting point). Which of the following is correct? a. He should start normal to the river bank. b. He should start in such a way that he moves normal to the bank, relative to the bank. c. He should start in a particular (calculated) direction making an obtuse angle with the direction of water current. d. The man cannot cross the river in that way. n. 11 .- 1 .11. 1 | 11 |

152 | How far will the car have traveled in the time? (in km) ( mathbf{A} cdot mathbf{6} ) B. 6.75 c. 7.75 D. 8.75 | 11 |

153 | A man running along a straight road with uniform velocity ( vec{u}=u hat{i} ) feels that the rain is falling vertically down along ( -hat{boldsymbol{j}} ). If he doubles his speed,he finds that the rain is coming at an angle ( theta ) with the vertical. The velocity of the rain with respect to the ground is : A ( . u i-u tan theta hat{j} ) B. ( u i-frac{u}{tan theta} ) c. ( u tan theta-u vec{j} ) D. ( frac{u}{tan theta} vec{i}-u vec{j} ) | 11 |

154 | An aeroplane moving horizontally at 20 ( mathrm{ms}^{-1} ) drops a bag. What is the displacement of the bag after 5 seconds ? Give ( left(g=10 mathrm{ms}^{-2}right) ) | 11 |

155 | Example 2.3 Two particles, 1 and 2 move with constant velocities v, and V2 along two mutually perpendicular straight lines towards the intersection point 0. At the moment t=0 the particles were located at the distance l, and l from the point O. How soon will the distance between the particles become the smallest? What is it equal to? Fig. 2.42 | 11 |

156 | Height of the cliff is ( A cdot 20 m ) B. 10 ( m ) ( c cdot 15 m ) D. 30 ( m ) | 11 |

157 | 11. An aircraft moving with a speed of 1000 km/h is at a height of 6000 m, just overhead of an anti-aircraft gun. If the muzzle velocity of the gun is 540 m/s, the firing angle for the bullet to hit the aircraft should be 972 km/h Vo = 540 m/s 6000 m TITUTI (a) 730 (6) 30° (c) 60° (d) 45° | 11 |

158 | A man standing on the road has to ho!d his umbrella at ( 30^{circ} ) with the vertical to keep the rain away. He throws the umbrella and starts running at 10 k ( m / h r . ) He find that rain drops are hitting his head vertically, then the speed of the rain drops with respect to moving man. A. ( 20 k m / h r ) в. ( 10 sqrt{3} k m / h r ) c. ( frac{10}{sqrt{3}} k m / h r ) D. ( 10 k m / h r ) | 11 |

159 | a. 41J cal plane is distances of the 59. The trajectory of a projectile in a vertical pl y = ax – bx”, where a and b are constants and are, respectively, horizontal and vertical distances projectile from the point of projection. The maxim height attained by the particle and the angle of project from the horizontal are 62 a. -, tan (b) b. , tan- (26) a tan- (a) do 2a tan(a) | 11 |

160 | A projectile is fired horizontally with a speed of ( 98 m s^{-1} ) from the top of a hill ( 490 m ) high. Find the magnitude of vertical velocity with which the projectile hits the ground. (Take ( boldsymbol{g}= ) ( left.9.8 m / s^{2}right) ) A ( cdot 98 m s^{-1} ) B. ( 40 mathrm{ms}^{-1} ) c. ( 116 mathrm{ms}^{-1} ) D. ( 196 mathrm{ms}^{-1} ) | 11 |

161 | * VE WCSc. 2. Given two vectors Ā== 3î + 4ſ and B == i + j. O is the angle between A and B. Which of the following statements is/are correct? i tj is the component of Ā along B. is the component of A perpendicular b. |ālsino (2 is the component of Ă perpendicular c. alcoso ( 2 ) is the component of à along B. to B 1 + d. Ä sin is the component of Ā perpendicular to B. | 11 |

162 | n Illustration 5.8 Two particles A and B are proie ome point in different directions in such a manner hot vertical components of their initial velocities are same (Fig. 5.8). Find the ratio of range. YA Fig. 5.8 | 11 |

163 | illustration 5.74 Find the angular velocity of A with respect to B in Fig. 5.156. Fig. 5.156 | 11 |

164 | A car ( A ) is going north-east at ( 80 mathrm{km} / mathrm{h} ) and another car ( B ) is going south-east at ( 60 mathrm{km} / mathrm{h} . ) Then the direction of the velocity of ( A ) relative to ( B ) makes with the north an ( alpha ) angle such that ( tan alpha ) is : A ( cdot frac{1}{7} ) B. ( frac{3}{4} ) ( c cdot frac{4}{3} ) D. ( frac{3}{5} ) | 11 |

165 | Illustration 5.7 A bullet with muzzle velocity 100 m 1. to be shot at a target 30 m away in the same horizontal li How high above the target must the rifle be aimed so that bullet will hit the target? 30 m Target Fig. 5.7 | 11 |

166 | Which of the following motions is different from the rest? A. a ball thrown horizontally in air B. a bomb released from a flying aeroplane c. a javelin thrown by an athlete D. a bird flying in the air | 11 |

167 | 17. To a man going with a speed of 5 ms, rain appears to be falling vertically. If the actual speed of rain is 10 ms, then what is the angle made by rain with the vertical? – 1 | 11 |

168 | A mass m rotates in a vertical circle of radius, ( R ) and has a circular speed ( v_{c} ) at the top.- If the radius of the circle is increased by a factor of ( 4, ) circular speed at the top will be A. decreased by a factor of 2 B. decreased by a factor of 4. c. increased by a factor of 2 D. increased by a factor of 4 | 11 |

169 | Consider the diagram of the trajectory of a thrown tomato. At what point is the kinetic energy least? | 11 |

170 | A gun fires a bullet. the barrel of the gun is inclined at an angle of ( 45^{circ} ) with horizontal. when the bullet leaves the barrel it will be travelling at an angle greater than ( 45^{circ} ) with horizontal. A. True B. False | 11 |

171 | If y denotes the displacement and t denote the time and the displacement is given by ( y=a sin t, ) the velocity of the particle is- | 11 |

172 | Illustration 5.43 A truck is moving with a constant velocity of 54 kmh. In what direction should a stone be projected up with a velocity of 20 ms, from the floor of the truck, so as to appear at right angles to the truck, for a person standing on earth? v = 20 ms? u= 15 ms Fig. 5.83 | 11 |

173 | An old man and a boy are walking towards each other and a bird is flying over them as shown in the figure. Find the velocity of bird as seen by the boy. A ( .12 hat{j} ) B. ( 16 hat{j} ) ( c .-12 hat{j} ) D. ( -16 hat{j} ) | 11 |

174 | The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is: A ( cdot 120^{circ} ) B . 135 ( c .90^{circ} ) D. ( 150^{circ} ) | 11 |

175 | In a uniform circular motion, the angle between the velocity and acceleration is ( mathbf{A} cdot mathbf{0} ) B . ( 45^{circ} ) ( c cdot 60^{circ} ) D. ( 75^{circ} ) E ( .90^{circ} ) | 11 |

176 | If the sum of two unit vector is a unit vector, then the magnitude of their difference is: A. ( sqrt{3} ) B. ( sqrt{2} ) c. ( sqrt{5} ) D. ( frac{1}{sqrt{2}} ) | 11 |

177 | Two uniform solid cylinders A and B each of mass 1 kg are connected by a spring of constant 200 Nm at their axles and are placed on a fixed wedge as shown in the Fig. 6.325. There is no friction between cylinders and wedge. The angle made by the line AB with the horizontal, in equilibrium, is A Moto B 160° 30° a. 0° c. 30° Fig. 6.325 b. 15° d. None of these | 11 |

178 | The velocity of a particle is ( boldsymbol{v}=boldsymbol{v}_{0}+ ) ( g t+f t^{2} . ) If its position is ( x=0 ) at ( t=0 ) then its displacement after unit time ( (t=1) ) is A ( cdot v_{0}+2 g+3 f ) в. ( v_{0}+frac{g}{2}+frac{f}{3} ) ( mathbf{c} cdot v_{0}+g+f ) D. ( v_{0}+frac{g}{2}+f ) | 11 |

179 | tilustration 5.70 The tangential acceleration of a particle moving in a circular path of radius 5 cm is 2 ms. The angular velocity of the particle increases from 10 rad s-to 20 rads- during some time. Find a. this duration of time and b. the number of revolutions completed during this time. | 11 |

180 | If ( boldsymbol{v}_{1} sin boldsymbol{theta}_{1}=boldsymbol{v}_{2} sin theta_{2}, ) then choose the incorrect statement A. The time of flight of both the particles will be same B. The maximum height attained by the particles will be same C. The trajectory of one with respect to another will be a horizontal straight line D. None of these | 11 |

181 | Tu possible in this case Two particles are projected simultaneously from the same pint with the same speed, in the same vertical plane, and at different angles with the horizontal in a uniform gravitational field acting vertically downwards. A frame of reference is fixed to one particle. The position vector of the other particle, as observed from this frame, is 7. Which of the following statements is correct? a. r is a constant vector. b. ř changes in magnitude as well as direction with time. c. The magnitude of r increases linearly with time; its direction does not change. d. The direction of r changes with time; its magnitude may or may not change, depending on the angles of projection. | 11 |

182 | CLIOL O NUUSUTIS WILT WU sono 26. A particle is projected from point A to hit an apple as shown in Fig. 5.195. The particle is directly aimed at the apple. Show that particle will not hit the apple. Now show that if the string with which the apple is hung is cut at the time of firing the particle, then the particle will hit the apple. Apple Fig. 5.195 | 11 |

183 | A person reaches a point directly opposite on the other bank of a river. The velocity of the water in the river is ( 4 m s^{-1} ) and the velocity of the person in still water is ( 5 m s^{-1} ). If the width of the river is ( 84.6 ~ m, ) time taken to cross the river in seconds is: A . 9.4 B. 2 c. 84.6 D. 28.2 | 11 |

184 | The moment of the force, ( overrightarrow{boldsymbol{F}}=mathbf{4} hat{mathbf{i}}+ ) ( 5 hat{j}-6 hat{k} ) at (2,0,-3) about the point ( (2,-2,-2), ) is given by ( mathbf{A} cdot-8 hat{i}-4 hat{j}-7 hat{k} ) B . ( -4 hat{i}-hat{j}-8 hat{k} ) ( mathbf{c} .-7 hat{i}-8 hat{j}-4 hat{k} ) D. ( -7 hat{i}-4 hat{j}-8 hat{k} ) | 11 |

185 | A ship moves at ( 40 mathrm{kmph} ) due north and suddenly moves towards east through ( 90^{0} ) and continues to move with the same speed. Then the change in velocity is A. zero B. 40 kmph North East c. ( 40 mathrm{kmph} ) south west D. ( 40 sqrt{2} ) kmph south East | 11 |

186 | Two boys enter a running escalator on the ground floor in a shopping mall and they do some fun on it. The first boy repeatedly follows ( p_{1}=1 ) step up and then ( q_{1}=2 ) steps down whereas the second boy repeatedly follows ( p_{2}=2 ) steps up and then ( q_{2}=1 ) step down. Both of them move relative to escalator with speed ( v_{r}=50 c m s^{-1} . ) If the first boy takes ( t_{1}=250 s ) and the second boy ( operatorname{takes} t_{2}=50 s ) to reach the first floor how fast is the escalator running? | 11 |

187 | A particle is revolving in a circular path of radius ( 200 m ) at a speed of ( 20 m / s . ) lts speed is increasing at the rate of ( sqrt{5} m / s^{2} . ) Its acceleration is ( mathbf{A} cdot 2 m / s^{2} ) В. ( sqrt{7} m / s^{2} ) c. ( 3 m / s^{2} ) D. ( sqrt{5} m / s^{2} ) | 11 |

188 | A particle at ( x=0 ) and ( t=0 ) starts moving along +ve X-direction with velocity v then x varies with time as? ( mathbf{A} cdot mathbf{t} ) в. ( t^{3} ) ( c cdot t^{2} ) D. ( t^{1 / 2} ) | 11 |

189 | Snow is falling vertically at a constant speed of ( 8.0 mathrm{m} / mathrm{s} . ) At what angle from the vertical do the snowflakes appear to be falling as viewed by the driver of a car travelling on a straight, level road with a speed of ( 50 mathrm{km} / mathrm{h} ) ? | 11 |

190 | A gun fires two bullets at ( 60^{circ} ) and ( 30^{circ} ) with the horizontal the bullets strike att same horizontal distance. The maximum heights for the two bullets are in the ratio A .2: 1 B. 3: 1 c. 4: 1 D. 1: 1 | 11 |

191 | Out of the following set of forces, the resultant of which cannot be zero? a. 10, 10, 10 b. 10, 10, 20 c. 10, 20, 20 d. 10, 20, 40 | 11 |

192 | If position vector of a point varies with time ” ( boldsymbol{t}^{prime prime} ) as ( overrightarrow{boldsymbol{r}}=left(boldsymbol{t}+boldsymbol{t}^{2}right)(hat{boldsymbol{i}}+hat{boldsymbol{j}}) ) meter then velocity at time ( t=4 s ) will be A ( cdot(6 hat{i}+6 hat{j}) m / s ) B . ( (6 hat{i}+9 hat{j}) m / s ) c. ( (9 hat{i}+6 hat{j}) m / s ) D. ( (9 hat{i}+9 hat{j}) m / s ) | 11 |

193 | Magnitude of vector ( hat{boldsymbol{i}}-hat{boldsymbol{j}} ) ( mathbf{A} cdot mathbf{0} ) B. ( sqrt{2} ) c. 1 D. 2 | 11 |

194 | 22. A body A is thrown vertically upwards with such a velocity that it reaches a maximum height of h. Simultaneously, another body B is dropped from height h. It strikes the ground and does not rebound. The velocity of A relative to B versus time graph is best represented by (upward direction is positive) a. VABN VAB VAB | 11 |

195 | A car travels 1000 meters north and the 1000 meters south. The entire trip takes 200 seconds. What is the car’s average velocity for the trip? A. ( 10 mathrm{m} / mathrm{s} ) в. ( 20 mathrm{m} / mathrm{s} ) c. ( 100 m / s ) D. ( 200,000 mathrm{m} / mathrm{s} ) E . ( 0 m / s ) | 11 |

196 | 11. An object has velocity v w.r.t. ground. An observer moving with constant velocity vo W.r.t.ground measures the velocity of the object as 72. The magnitudes of three velocities are related by a. Vo ? 1 + v2 b. V SV2 + Vo c. 12 2 11+ Vo d. All of the above | 11 |

197 | 31. Shortest distance between them subsequently is a. 18 m b. 15 m c. 25 m d. 8m | 11 |

198 | nan wants to swim in a river from A to ack from B to A always following line AB (Fig. 5.94). n points A and B is S. The velocity of the nt v is constant over the entire width of the river. AB makes an angle a with the direction of current. man moves with velocity u at angle B to the line AB. Ine man swim to cover distance AB and back, find the time to complete the journey. Illustration 5.50 A man wants to swim in B and back from B to A always foll The distance between points A and B is S. The vel river current v is constant over the The line AB makes an angle Fig. 5.94 | 11 |

199 | A ball is thrown from a point on ground at some angle of projection. At the time a bird starts from a point directly above this point of projection at a height ( h ) horizontally with speed ( u ). Given that in its flight ball just touches the bird at one point. Find the distance on ground where ball strikes: ( sqrt[4]{2 u} sqrt{frac{h}{g}} ) в. ( u sqrt{frac{2 h}{g}} ) c. ( 2 u sqrt{frac{2 h}{g}} ) ( u sqrt{frac{h}{g}} ) | 11 |

200 | A man can swim with a speed of 4.0 ( k m / h r ) in still water. How long does he take to cross a river ( 1.0 mathrm{km} ) wide, if the river flows steadily at ( 3.0 mathrm{km} / mathrm{hr} ) and he makes his strokes normal to the river current? How far down the river does he go, when he reaches the other bank? | 11 |

201 | I SOUVvE ou CIVIL 8. A person goes 10 km north and 20 km east. What will be displacement from initial point? (a) 22.36 km (b) 2 km (c) 5 km (d) 20 km | 11 |

202 | If ( vec{a}=hat{i}+2 hat{j}+2 hat{k} ) and ( vec{b}=3 hat{i}+6 hat{j}+ ) ( 2 hat{k}, ) then a vector in the direction of ( vec{a} ) and having magnitude as ( |vec{b}| ) is A ( cdot 7(hat{i}+hat{j}+hat{k}) ) B ( cdot frac{7}{3}(hat{i}+2 hat{j}+2 hat{k}) ) c. ( frac{7}{9}(hat{i}+2 hat{j}+2 hat{k}) ) D. none of these | 11 |

203 | It is possible for a body to move in a circular path with uniform speed as long as it is travelling A. equal distances in equal interval of time B. unequal distances in unequal interval of time c. equal distances in unequal interval of time D. unequal distances in equal interval of time | 11 |

204 | 46. The sum of the magnitudes of two forces acting at a point is 16 N. The resultant of these forces is perpendicular to the smaller force and has a magnitude of 8 N. If the smaller force is of magnitude x, then the value of x is a. 2N b. 4N C. 6N d. 7 N | 11 |

205 | A body moving in a circular path with constant speed is an accelerated motion. Why? | 11 |

206 | Define uniform circular motion. A particle is travelling in a circle of diameter ( 15 m ). Calculate the distance covered and the displacement when it completes two rounds. | 11 |

207 | Mark the following statement is true or false. A ball thrown vertically up takes more | 11 |

208 | Which of the following quantity remains constant in a uniform circular motion? A. velocity B. speedd c. both velocity and speed D. none of these | 11 |

209 | Wind is blowing west to east along two parallel tracks. Two trains moving with same speed in opposite directions have the relative velocity with respect to wind in the ratio ( 1: 2 . ) The speed of each train is A. equal to that of wind B. double that of wind c. three times that of wind D. half that of wind | 11 |

210 | 7. The maximum height reached by the ball as measured from the ground would be a. 52 m b. 31.25 m c. 83.25 m d. 63.25 m | 11 |

211 | An aeroplane flying at a constant speed releases a bomb. As the bomb moves away from the aeroplane, it will A. always be vertically below the aeroplane only if the aeroplane was flying horizontally B. always be vertically below the aeroplane only if the aeroplane was flying at an angle of ( 45^{circ} ) to the horizontal c. always be vertically below the aeroplane D. gradually fall behind the aeroplane if the aeroplane was flying horizontally | 11 |

212 | The velocity of a particle is ( boldsymbol{v}=boldsymbol{v}_{0}+ ) ( g t+f t^{2} . ) If its position is ( x=0 ) at ( t=0 ) then its displacement after unit time ( (t=1) ) is: A ( cdot v_{0}+2 g+3 f ) B . ( v_{0}+g / 2+f / 3 ) ( mathbf{c} cdot v_{0}+g+f ) D . ( v_{0}+g / 2+f ) | 11 |

213 | Two particles ( A ) and ( B ) are moving in a horizontal place anticlockwise on two different concentric circles with different constant angular velocities ( 2 omega ) and ( omega ) respectively. Find the relative velocity (in ( m s ) ) of ( B ) w.r.t ( A ) after time ( boldsymbol{t}=boldsymbol{pi} / omega . ) They both start at the position as shown in figure (Take ( omega= ) 3 radsec, ( r=2 m ) | 11 |

214 | Illustration 3.3 Two equal forces have their resultant equal to either. At what angle are they inclined? | 11 |

215 | Compare the motion of a body dropped to that of a horizontal projectile, both falling from the same height. | 11 |

216 | A body is projected horizontally from a point above the ground and motion of the body is described by the equation ( boldsymbol{x}=mathbf{2} boldsymbol{t}, boldsymbol{y}=mathbf{5} boldsymbol{t}^{2} ) where ( boldsymbol{x}, ) and ( boldsymbol{y} ) are horizontal and vertical coordinates in meter after time ( t . ) The initial velocity of the body will be A. ( sqrt{29} mathrm{m} / mathrm{s} ) horizontal B . ( 5 mathrm{m} / mathrm{s} ) horizontal c. ( 2 m / s ) vertical D. ( 2 m / s ) horizontal | 11 |

217 | A shell is fired from a cannon with a speed of ( 100 mathrm{m} / mathrm{s} ) at an angle ( 30^{circ} ) with the horizontal (positive ( y- ) direction). At the highest point of its trajectory, the shell explodes into two equal fragments of masses in the ratio ( 1: 2 . ) The lighter fragment moves vertically upwards with an initial speed of ( 200 mathrm{m} / mathrm{s} ). What is the speed of the other fragment at the time of explosion? | 11 |

218 | Find the ( x- ) coordinate of the particle at the moment of time ( t=20 s ) A. ( -4.0 m ) в. ( -3.0 m ) c. ( 4.0 m ) D. ( -2.0 m ) | 11 |

219 | Jo 10. 200 . JOM N 32. A cannon fires a projectile as shown in Fig. A.14. The dashed line shows the trajectory in the absence of gravity. The points M, N, O, and P correspond to time at t= 0,1 s, 2 s M and 3 s, respectively. The lengths of Fig. A.14 X, Y, and Z are, respectively, a. 5 m, 10 m, 15 m b. 10 m, 40 m, 90 m c. 5 m, 20 m, 45 m d. 10 m, 20 m, 30 m SM- | 11 |

220 | If the speed of body moving in circle is doubled and the radius is halved, its centripetal acceleration becomes A. Eight times B. Four times c. Two times D. Sixteen times | 11 |

221 | The radius of the Earth is approximately ( 6.4 times 10^{6} m . ) The instantaneous velocity of a point on the surface of the Earth at the equator is ( 4.672 times 10^{x} ). Find the value of ( mathbf{x}: ) | 11 |

222 | At the highest point of a projectile its velocity i half the initial velocity in magnitude The angle of projection from ground is A ( .30^{circ} ) В . ( 45^{circ} ) ( c cdot 60^{circ} ) D. ( 90^{circ} ) | 11 |

223 | The velocity of a particle is zero at time ( t=2, ) then A. displacement must be zero in the interval ( t=0 ) to ( t= ) 2 B. acceleration may be zero at ( t=2 ) c. velocity must be zero for ( t>2 ) D. acceleration must be zero at ( t=2 ) | 11 |

224 | A particle moves from ( A ) to ( B ) such that ( boldsymbol{x}=boldsymbol{t}^{2}+boldsymbol{t}-mathbf{3} . ) Its average velocity from ( t=2 s ) to ( t=5 s ) is ( A cdot 6 m s^{-1} ) 3. ( 8 m s^{-1} ) ( c cdot 8.5 m s^{-1} ) D. ( 7 mathrm{ms}^{-1} ) | 11 |

225 | A circular platform is mounted on a frictionless vertical axle. Its radius ( mathrm{R}=2 mathrm{m} ) and its moment of inertia about the axle is ( 200 k g m^{2} ). It is initially at rest. A ( 50 mathrm{kg} ) man stands on the edge of the platform and begins to walk along the edge at the speed of ( 1 mathrm{ms}^{-1} ) relative to the ground. Time taken by the man to compete one revolution with respect to disc is: ( mathbf{A} cdot pi s ) B . ( frac{3 pi}{2} s ) ( mathbf{c} cdot 2 pi s ) D. ( frac{pi}{2} s ) | 11 |

226 | If ( |bar{A}+bar{B}|=|bar{A}|+|bar{B}| ) then the angle between ( bar{A} ) and ( bar{B} ) is: ( A cdot 0^{0} ) B . ( 90^{circ} ) ( c cdot 180^{circ} ) D. ( 60^{circ} ) | 11 |

227 | 4. The drift of the man along the direction of flow, when he arrives at the opposite bank is a. b. 673 cm a. 1 km 673 km c. 3/3 km km | 11 |

228 | A solid sphere is rolling on a rough surface, whose centre of mass is at ( C ) at a certain instant. Find at that instant it has angular velocity ( omega ) Its radius is ( mathrm{R} ). Find the angular acceleration at that instant mass of sphere is ( mathrm{m} ) A ( frac{5}{2} frac{g d}{R^{2}} ) В ( frac{5}{7} frac{g d}{R^{2}} ) c. ( frac{5}{2} frac{dleft(g+omega^{2} Rright)}{R^{2}} ) ( D ) | 11 |

229 | 6. Two guns are mounted (fixed) on two vertical cliffs that are very high from the ground as shown in figure. The muzzle velocity of the shell from G, is u, and that from G, is uz The guns aim exactly towards each other The ratio u, :u such that the shells collide with each other in air is (Assume that there is no resistance of air) Gaui (a) 1:2 (b) 1:4 (c) will not collide for any ratio (d) will collide for any ratio | 11 |

230 | In the above problem, the angular acceleration of the particle at ( t=2 sec ) is rads( ^{-2} ) A ( cdot 14 ) B. 16 ( c cdot 18 ) D. 24 | 11 |

231 | Consider the two vectors ( vec{A}=3 hat{i}-2 hat{j} ) and ( vec{B}=-hat{i}-4 hat{j} . ) Calculate ( (a) vec{A}+ ) ( overrightarrow{boldsymbol{B}} cdot(boldsymbol{b}) overrightarrow{boldsymbol{A}}-overrightarrow{boldsymbol{B}} ) ( (c)|overrightarrow{boldsymbol{A}}+overrightarrow{boldsymbol{B}}| cdot(boldsymbol{d})|overrightarrow{boldsymbol{A}}-overrightarrow{boldsymbol{B}}| ) and ( (e) ) the directions of ( vec{A}+vec{B} ) and ( overrightarrow{boldsymbol{A}}-overrightarrow{boldsymbol{B}} ) | 11 |

232 | A particle is going in a spiral path as shown in Fig. with constant speed. Then A. its velocity is constant B. its acceleration is constant C. magnitude of its acceleration is constant D. The magnitude of acceleration decreases continuously | 11 |

233 | A triangle has sides of length 13,30 and ( 37 . ) If the radius of the inscribed circle is ( frac{p}{q}(text { where } p text { and } q text { are coprime }) ),then the value of ( boldsymbol{q}^{boldsymbol{p}+mathbf{3}} ) is A . 2048 в. 4096 c. 1024 D. 512 | 11 |

234 | Mark the correct statement(s): A. The magnitude of the velocity of particle is equal to its speed B. The magnitude of average velocity in an interval is equal to its average speed in that interval. C. It is possible to have a situation in which the speed of a particle is always zero but the average speed is not zero. D. It is possible to have a situation in which the speed of the particle is never zero but the average speed in an interval is zero. | 11 |

235 | An aeroplane is flying in a horizontal direction with a velocity ( 600 mathrm{km} / mathrm{h} ) at height of 1960 m. When it is vertically above the point ( A ) on the ground, a body is dropped from it. The body strikes the ground at point B. Calculate the distance AB. | 11 |

236 | In circular motion of a particle, This question has multiple correct options A. particle cannot have uniform motion B. particle cannot have uniformly accelerated motion C . particle cannot have net force equal to zero D. particle cannot have any force in tangential direction | 11 |

237 | An object is thrown into space horizontally under the action of earth’s gravity. Then the object is said to be a : A. projectile B. trajectory c. spaceship D. none of these | 11 |

238 | top Q Type your question Ball ( X ) has an initial velocity of ( 3.0 m s^{-1} ) in a direction along line ( A B ) Ball ( Y ) has a mass of ( 2.5 k g ) and an initial velocity of ( 9.6 m s^{-1} ) in a direction at an angle of ( 60^{circ} ) to line ( A B ) The two balls collide at point ( B ). The balls stick together and then trave along the horizontal surface in a direction at right-angles to the line ( boldsymbol{A B} ) as shown in Fig. Determine the difference between the | 11 |

239 | body is projected with a velocity of 60 ms at 30° to horizontal Column I Column II Initial velocity vector a. 60/3 + 40ĵ Velocity after 3 s 30/3ỉ +10j Displacement after c. 30.3 + 30 2 s iv. iv. Velocity after 2 s d. 3053 | 11 |

240 | A boat crossing a river moves with a velocity v relative to still water. The river is flowing with a velocity v/2 with respect to the bank. The angle with respectively the slow direction with which the boat should move to minimize the drift is A ( .30^{circ} ) B. ( 60^{circ} ) ( c cdot 180^{circ} ) D. ( 120^{circ} ) | 11 |

241 | The wind appears to blow from north to a man moving in the north-east direction. When he doubles his velocity, the wind appears to move in the direction cot ( ^{-1} ) (2) east of north. If the actual magnitude of velocity of the wind is ( V=frac{1}{sqrt{x}} times ) magnitude of velocity of man and direction along east. Find ( x ) | 11 |

242 | Statement 1: The magnitude of velocity of two boats relative to river is same. Both starts simultaneously from same point on one bank and they may reach opposite bank simultaneously moving along different paths. Statement 2: For boats to cross the river in same time.The component of their velocity relative to river in direction normal to flow should be same. A. Statement-1 is false, Statement- 2 is true B. Statement-1 is true, Statement-2 is true, Statementis a correct explanation for statement- – c. statement-1 is true, statement- 2 is true; statementis not a correct explanation for statement- D. Statement-1 is true, Statement-2 is false. | 11 |

243 | The positive vector of a particle is determined by the expression ( vec{r}= ) ( 3 t^{2} hat{i}+4 t^{2} hat{j}+7 hat{k} . ) The distance traversed in first 10 sec is: A. ( 500 mathrm{m} ) B. 300 ( m ) c. ( 150 mathrm{m} ) D. ( 100 mathrm{m} ) | 11 |

244 | A stone is projected from the ground with a velocity of ( 14 mathrm{ms}^{-1} . ) One second later it clears a wall ( 2 m ) high. The angle of projection is ( left(boldsymbol{g}=mathbf{1 0} boldsymbol{m} boldsymbol{s}^{-2}right) ) A ( cdot 45^{circ} ) B. ( 30^{circ} ) ( c cdot 60^{circ} ) D. ( 15^{circ} ) | 11 |

245 | Illustration 3.25 An insect crawls from A to B where B is the center of the rectangular slant face. Find the (a) initial and final position vector of the insect and (b) displacement vector of the insect. (0,2,0) (0,2,0) 3 1 BI 2″ 2) (0, 2, 1) (3.0,0) (3,0,0) z/ (0,0,1) z (0,0,1) Fig. 3.49 (3,0,1) | 11 |

246 | 4. In 1.0 s, a particle goes from point A to point a B, moving in a semicircle of radius 1.0 m (Fig. A.48). The magnitude of the average velocity 1.0 m is a. 3.14 ms- c. 1.0 ms-1 b. 2.0 ms d. Zero Fig. A.51 (IIT JEE, 1999) 11 1 doboro the | 11 |

247 | A projectile is fired with a velocity ( u ) at angle ( theta ) with the ground surface. During the motion at any time it is making an angle ( alpha ) with the ground surface. The speed of particle at this time will be A . ucostheta( theta )seca B. ucostheta.tana c. ( u^{2} cos ^{2} alpha sin ^{2} alpha ) D. usintheta.sina | 11 |

248 | Same force acts on two bodies of different masses ( 2 k g ) and ( 4 k g ) initially at rest. The ratio of times required to acquire same final velocity is:- A .2: 1 B. 1: 2 ( c cdot 1: 1 ) D. 4: 16 | 11 |

249 | A large number of particles are moving towards each other with velocity ( V ) having directions of motion randomly distributed. What is the average relative velocity between any two particles averaged over all the pairs? A. ( 4 V / pi ) в. ( 4 pi V ) ( c cdot V ) D. ( pi V / 4 ) | 11 |

250 | A popular game in Indian villages is goli which is played with small glass balls called golis. The goli of one player is situated at a distance of ( 2.0 mathrm{m} ) from the goli of the second player. This second player has to project his goli by keeping the thumb of the left hand at the place of his goli, holding the goli between his two middle fingers and making the throw. If the projected goli hits the goli of the first player, the second player wins. If the height from which the goli is projected is ( 19.6 mathrm{cm} ) from the ground and the goli is to be projected horizontally, with what speed should it be projected so that it directly hits the stationary goli without falling on the ground earlier? | 11 |

251 | An object starts from rest, and moves under the acceleration ( overrightarrow{boldsymbol{a}}=mathbf{4} hat{mathbf{i}} ). Its position after ( 3 s ) is given by ( vec{r}= ) ( (7 hat{i}+4 hat{j}) . ) What is its initial position? | 11 |

252 | A swimmer swims in still water at a speed ( =5 k m / h . ) He enters a ( 200 m ) wide river, having river flow speed ( = ) ( 4 k m / h r ) at point ( A ) and proceeds to swim at an angle of ( 127^{circ} ) with the river flow direction. Another point B is located directly across ( A ) on the other side. The swimmer lands on the other bank at a point ( C, ) from which he walks the distance ( mathrm{CB} ) with a speed ( =3 k m / h r ) The total time in which he reaches from ( A ) to ( B ) is A . 5 minutes B. 4 minutes c. 3 minutes D. none | 11 |

253 | A spaceship rotating around earth with a constant speed experiences acceleration towards A. against the instantaneous direction of velocity of spaceship B. in the instantaneous direction of velocity of spaceship c. center of the earth D. away from the center of the earth | 11 |

254 | List List II A) Constant I) At highest point speed and varying ( quad ) of body velocity ( quad ) projected vertically up B) Zero II) Uniform displacement and ( quad ) circular motion finite distance III) At any C) Zero velocity ( quad ) intermediate point of and finite acceleration ( quad ) freely falling body D) Non-zero IV) Body on reaching point of velocity and nonzero acceleration The correct match is: ( A cdot A-|V, B-| I, C-|I|, D-1 ) B. ( A-11, B-1 V, C-1, D-11 ) ( mathbf{C} cdot A-|I, B-I, C-I V, D-| ) D. ( A-1, B-111, C-11, D-1 V ) | 11 |

255 | A car is traveling with linear velocity on a circular road of radius ( r ). If it is increasing its speed at the rate of ‘a’ ( m s^{-2}, ) then the resultant acceleration will be A ( cdot sqrt{frac{v^{4}}{r^{2}}+a^{2}} ) B. ( sqrt{frac{v^{4}}{r^{2}}-a^{2}} ) c. ( sqrt{frac{v^{2}}{r^{2}}+a^{2}} ) D. ( sqrt{frac{v^{2}}{r^{2}}-a^{2}} ) | 11 |

256 | The horizontal distance between two bodies, when their velocity are perpendicular to each other, is A. ( 1 m ) B. ( 0.5 mathrm{m} ) ( c .2 m ) D. ( 4 m ) | 11 |

257 | Two particles of masses ( m ) and ( 2 m ) are kept at a distance a. Find their relative velocity of approach when separation becomes ( a / 2 ) ( mathbf{1} ) 2 A ( cdot 2 sqrt{frac{3 a}{2 G M}} ) B. ( sqrt{frac{a}{2 G M}} ) ( ^{mathbf{C}} cdot 2 sqrt{frac{2 G M}{3 a}} ) D. ( sqrt{frac{6 G M}{a}} ) | 11 |

258 | A vector perpendicular to ( hat{i}+hat{j}+hat{k} ) is ( mathbf{A} cdot hat{i}-hat{j}+hat{k} ) B. ( hat{i}-hat{j}-hat{k} ) c. ( -hat{i}-hat{j}-hat{k} ) D. ( 3 hat{i}+2 hat{j}-5 hat{k} ) | 11 |

259 | A body is moving down into a well through a rope passing over a fixed pulley of radius ( 10 mathrm{cm} . ) Assume that there is no slipping between rope ( & ) pulley, calculate the angular velocity and angular acceleration of the pulley at an instant when the body is going down at a speed of ( 20 mathrm{cm} / mathrm{s} ) and has an acceleration of ( 4.0 m / s^{2} ) | 11 |

260 | 47. A ball is projected from the ground at angle o w horizontal. After 1 s, it is moving at angle 45 horizontal and after 2 s it is moving horizontally. What the velocity of projection of the ball? a. 10/3 ms-1 b. 20/3 ms-1 c. 1075 ms -1 d. 202 ms-1 | 11 |

261 | A small sphere is projected with a velocity of 3 ms-‘ in a direction 60° from the horizontal y-axis, on the smooth inclined plane (Fig. 5.197). The motion of sphere takes place in the x-y plane. Calculate the magnitude v of its velocity after 2 s. R $60º – Y 30°7 Fig. 5.197 | 11 |

262 | The velocity with which particle strikes the plane ( boldsymbol{O B} ) A ( cdot 15 mathrm{ms}^{-1} ) B. ( 30 m s^{-1} ) ( c cdot 20 m s^{-1} ) D. ( 10 mathrm{ms}^{-1} ) | 11 |

263 | 19. The velocity with which particle strikes the plane OB, a. 15 ms- b. 30 ms c. 20 ms- d. 10 ms- ca: 11 | 11 |

264 | In the projectile motion shown is figure, ( operatorname{given} t_{A B}=2 s ) then which of the folowing is correct ( :left(g=10 m s^{-2}right) ) his question has multiple correct options A. particle is at point B at 3 s B. maximum height of projectile is 20 m c. initial vertical component of velocity is ( 20 mathrm{ms} ) D. horizontal component of velocity is ( 20 mathrm{ms} ) | 11 |

265 | 1. Statement I: The projectile has only vertical component of velocity at the highest point of its trajectory. Statement II: At the highest point, only one component of velocity is present. | 11 |

266 | When a man is standing, rain drops appear to him falling at ( 60^{circ} ) from the horizontal from his front side. When he is travelling at ( 5 k m / h ) on a horizontal road, they appear to him falling at ( 30^{circ} ) from the horizontal from his front side. The actual speed of the rain in ( k m / h ) is. A . 3 B. 4 ( c .5 ) D. 6 | 11 |

267 | The time in which a force of ( 2 N ) produces a change in momentum of ( 0.4 k g m s^{-1} ) in the body is A . ( 0.2 s ) в. 0.02 c. ( 0.5 s ) D. ( 0.05 s ) | 11 |

268 | The length of hour hand of a wrist watch is ( 1.5 mathrm{cm} . ) Find magnitude of angular acceleration? A. ( 0 r a d / s e c^{2} ) B. ( 2 pi r a d / s e c^{2} ) C ( .2 mathrm{rad} / mathrm{sec}^{2} ) D. ( 1 r a d / s e c^{2} ) | 11 |

269 | 14. The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the magnitudes of forces? (a) 12,5 (b) 14,4 (c) 5,13 (d) 10,8 | 11 |

270 | A person standing on a road has to hold his umbrella at ( 60^{circ} ) with the vertical to keep the rain away. He throws the umbrella and starts running at ( 20 m s^{-1} ) He find that rain drops are hitting his head vertically. Find the speed of the rain drops with respect to (a) the road and (b) the moving person. | 11 |

271 | The positions of a particle moving along a straight line are ( x_{1}=50 mathrm{m} ) at 10.30 a.m. and ( x_{2}=55 mathrm{m} ) at 10.35 a.m. respectively. What is the displacement of the particle between 10.30 a.m. and 10.35 a.m.? ( A cdot 2 m ) B. ( 5 mathrm{m} ) ( c cdot 7 m ) D. ( 9 mathrm{m} ) | 11 |

272 | A stone tied to the end of a string which is ( 80 mathrm{cm} ) long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in ( 25 s ), what is the magnitude of centripetal acceleration? ( left(operatorname{in} boldsymbol{m} / boldsymbol{s}^{2}right) ) A . 9.91 B . 2.36 c. 10.36 D. 12.69 | 11 |

273 | The sun revolves around galaxy with speed of ( 250 k m / s ) around the center of milky way and its radius is ( 3 times 10^{4} ) light year. The mass of milky way in ( k g ) is A ( cdot 6 times 10^{4} ) В ( .5 times 10^{4} ) ( c cdot 4 times 10^{4} ) D. ( 3 times 10^{4} ) | 11 |

274 | Which of the following is an example of uniform circular motion? A. The planet Pluto in its wandering about the sun B. The swing of a pendulum between the turning points C. A bug sitting still at the centre of a playing 50 rpm record D. The weights on the rim of a car tire as the car slowly accelerates | 11 |

275 | A car goes around uniform circular track of radius ( R ) at a uniform speed ( v ) once in every ( T ) seconds. The magnitude of the centripetal acceleration is ( a_{C} ). If the car now goes uniformly around a larger circular track of radius ( 2 R ) and experiences a centripetal acceleration of magnitude ( 8 a_{c}, ) then its time period is A . ( 2 T ) в. ( 3 T ) c. ( T / 2 ) D. 3 / 27 | 11 |

276 | In circular motion if ( bar{v} ) is velocity vector, ( bar{a} ) is acceleration vector, ( bar{r} ) is instantaneous position vector, ( bar{p} ) is momentum vector and ( bar{omega} ) is angular velocity of particle, then: This question has multiple correct options A ( . bar{v}, bar{omega}, bar{r} ) are mutually perpendicular B . ( bar{p}, bar{v}, bar{omega} ) are mutually perpendicular c. ( bar{r} times bar{v}=0 ) and ( bar{r} times bar{omega}=0 ) D. ( bar{r} . bar{v}=0 ) and ( bar{r} . bar{omega}=0 ) | 11 |

277 | If the displacement of a particle varies with time as ( sqrt{x}=t+7, ) which of the following statements is(are) true? This question has multiple correct options A. Velocity of the particle is inversely proportional to ( t ). B. Velocity of the particle is proportional to ( t ) C. Velocity of the particle is proportional to ( sqrt{t} ) D. The particle moves with a constant accelera | 11 |

278 | The position of a particle along along ( x ) axis is given by ( x=a+b t^{2}, ) where ( a= ) ( 8.5 mathrm{m}, mathrm{b}=2.5 mathrm{m} ) and ( t ) is in seconds. What is its average velocity at ( t=2.0 ) s? What will be its average velocity between ( t=2 s & t=4 s ? ) | 11 |

279 | Two particles are simultaneously projected in the horizontal direction from a point ( boldsymbol{P} ) at a certain height. The initial velocities of the particles are oppositely directed to each other and have magnitude v each. The separation between the particles at a time when their position vectors (drawn from the point ( P ) ) are mutually perpendicular, is ( ^{mathrm{A}} cdot frac{v^{2}}{2 g g} ) В. ( frac{v^{2}}{g} ) c. ( frac{4 v^{2}}{g} ) D. ( frac{2 v^{2}}{g} ) | 11 |

280 | Assertion Time taken by the bomb to reach the ground from a moving aeroplane depends on height of aeroplane only. Reason Horizontal component of velocity of the bomb remains constant and vertical component of bomb changes due to gravity. A. Both Assertion and Reason are true and the Reason is correct explanation of the Assertion. B. Both Assertion and Reason are true, but Reason is not correct explanation of the Assertion. C. Assertion is true, but the Reason is false D. Assertion is false, but the Reason is true. | 11 |

281 | (0) 21 dl II 5. If vectors P, Q and R have magnitude 5, 12 and 13 units and + + = Ã, the angle between Q and Ris (a) cos (b) cos (c) cos112 (d) cos -1 131 | 11 |

282 | Illustration 5.14 From a point on the ground at a distance a from the foot of a pole, a ball is thrown at an angle of 45°, which just touches the top of the pole and strikes the ground at a distance of b, on the other side of it. Find the height of the pole. | 11 |

283 | The relation between the time of flight of projectile ( T, ) and the time to reach the maximum height ( t_{m} ) is A ( cdot T_{f}=2 t_{m} ) B . ( T_{f}=t_{m} ) c. ( T_{f}=t_{m} / 2 ) ( mathbf{D} cdot T_{f}=sqrt{2} t_{m} ) | 11 |

284 | A swimmer wishes to cross a ( 500 mathrm{m} ) wide river flowing at ( 5 mathrm{km} / mathrm{h} ). His speed with respect to water is ( 3 mathrm{km} / mathrm{h} ). (a) If he heads in a direction making an angle ( theta ) with the flow, find the time he takes to cross the river.(b) Find the shortest possible time to cross the river. | 11 |

285 | In a uniform circular motion, radial acceleration is due to A. Change in position of the particle along ( X ) axis B. Change in position of the particle along Y axis C. Change in direction of tangential velocity D. Change in magnitude of tangential velocity | 11 |

286 | Illustration 5.17 A rubber ball escapes from the horizontal roof with a velocity – 5 ms. The roof is situated at a height, ha 20 m. If the length of each cnr is equal to X 4 m, with which car will the ball hit? Fig. 5.21 | 11 |

287 | Position of a particle in a rectangular coordinate system is (3,2,5) . Then its position vector will be A ( cdot 3 hat{i}+5 hat{j}+hat{k} ) B ( cdot 3 hat{i}+2 hat{j}+5 hat{k} ) c. ( 5 hat{i}+3 j+2 hat{k} ) D. None of tese | 11 |

288 | CE and DF are two walls of equal height (20 meter) from which two particles ( A ) and ( mathrm{B} ) of same mass are projected as shown in the figure.A is projected horizontally towards left while B is projected at an angle ( 37^{0} ) (with horizontal towards left) with velocity ( 15 ~ m / s e c ). If ( A ) always sees ( B ) to be moving perpendicular to EF, then the range of A on ground is A ( .24 m ) в. ( 30 m ) ( c .26 m ) D. ( 28 m ) | 11 |

289 | A body moving along a circular path will have : A. a constant speed B. a constant velocity c. no tangential velocity D. a radial acceleration | 11 |

290 | The smallest distance between the planes and the time when this occurs are: (nearly) ( left(operatorname{given} tan ^{-1}left(frac{128}{252}right)=tan ^{-1}left(26.9^{0}right)right) ) A. ( 54 mathrm{km}, 98 mathrm{s} ) B. ( 98 mathrm{km}, 54 mathrm{s} ) ( c .27 mathrm{km}, 189 mathrm{s} ) D. ( 189 mathrm{km}, 54 mathrm{s} ) | 11 |

291 | 8. Two forces, each equal to F, act as shown in Fig. 3.78. Their resultant is 1600 Fig. 3.78 b. F ن نه d. 15F . . … | 11 |

292 | A stationary wheel starts rotating about its own axis at a constant angular acceleration. If the wheel completes 50 rotations in the first ( 2 s, ) then the number of rotations made by it in the next ( 2 s ) is: A . 75 в. 100 c. 125 D. 150 | 11 |

293 | U. MIVUUNI 15 M lown over by 7. A particle is dropped from a tower in a unit gravitational field at t = 0. The particle is blown ou a horizontal wind with constant velocity. The slope om the trajectory of the particle with horizontal and its kiner energy vary according to curves. Here, x is the horizontal displacement and h is the height of particle from ground at time t. a. b. ſ KE | 11 |

294 | 16. A student throws soft balls out of the window at different angles to the horizontal. All soft balls have the same initial speed v= 10/3 ms. It turns out that all soft balls’ landing velocities make angles 30° or greater with the horizontal. Find the height h (in m) of the window above the ground. | 11 |

295 | A particle is projected with a speed u at an angle ( theta ) with the horizontal. What is the radius of curvature of the parabola traced out by the projectile at a point where the particle velocity makes an ( boldsymbol{theta} ) angle ( frac{-}{2} ) with the horizontal | 11 |

296 | A particle of mass ‘m’ is projected with a velocity ‘u’ at an angle ‘ ( boldsymbol{theta}^{prime} ) with the horizontal. Work done by gravity during its descent from its highest point to a point which is at half the maximum height is? A. none of these B. ( frac{m u^{2} sin ^{2} theta}{4} ) c. ( frac{1}{2} m u^{2} sin ^{2} theta ) D ( cdot frac{1}{2} m u^{2} cos ^{2} theta ) | 11 |

297 | A particle moves in the ( x ) -y plane with velocity ( v_{x}=8 t-2 ) and ( v_{y}=2 . ) If it passes through the point ( x=14 ) and ( boldsymbol{y}=mathbf{4} ) at ( boldsymbol{t}=mathbf{2 s}, ) the equation of the path is? A. ( x=y^{2}-y+2 ) В. ( x=y^{2}-2 ) c. ( x=y^{2}+y-6 ) D. None of these | 11 |

298 | Find the time dependence of the velocity of the particle. A ( cdot v=frac{alpha t}{4} ) B. ( v=frac{alpha^{2} t}{2} ) ( ^{mathrm{C}} cdot_{v}=frac{alpha^{2} t}{4} ) D. ( v=frac{alpha t}{2} ) | 11 |

299 | NO 28. A target is fixed on the top of a tower 13 m high. A person standing at a distance of 50 m from the pole is capable of projecting a stone with a velocity 10/8 ms. If he wants to strike the target in shortest possible time, at what angle should he project the stone? 20 | 11 |

300 | An athlete completes one round of a circular track of radius ( boldsymbol{R} ) in ( mathbf{4 0} boldsymbol{s} ). His displacement at the end of 2 minutes will be A ( .2 pi R ) в. ( 6 pi R ) ( c .2 R ) D. Zero | 11 |

301 | Position of a particle moving along ( boldsymbol{x}- ) axis is given by ( boldsymbol{x}=mathbf{3}(mathbf{2} boldsymbol{t}-mathbf{3})+mathbf{4}(mathbf{2} boldsymbol{t}- ) 3)( ^{2} ) Which of the following is correct about the particle? A. Initial speed is ( 21 mathrm{m} / mathrm{s} ) B. Initial speed is ( 18 mathrm{m} / mathrm{s} ) c. Initial speed is ( 42 mathrm{m} / mathrm{s} ) D. Acceleration is ( 8 mathrm{m} / mathrm{s} ) | 11 |

302 | 10. A swimmer wishes to cross a 500-m river flowing at 5 kmh. His speed with respect to water is 3 kmh. The shortest possible time to cross the river is a. 10 min b. 20 min c. 6 min d. 7.5 min | 11 |

303 | If ( |vec{A}+vec{B}|=|vec{A}-vec{B}|, ) then the angle between ( vec{A} ) and ( vec{B} ) will be ( A cdot 30^{circ} ) B . 45 ( c cdot 60 ) D. 90 | 11 |

304 | 6. A projectile is fired with velocity vo from a gun adjusted for a maximum range. It passes through two points P and Q whose heights above the horizontal are h each. Show that the separation of the two points is | 11 |

305 | A trolley is moving horizontally with a velocity of ( v ) m/s w.r.t. earth. A man starts running in the direction of motion of trolley from one end of trolley with a velocity ( 1.5 v ) m/ ( s ) w.r.t. the trolley. After reaching the opposite end, the man turns back and continues running with a velocity of1.5 ( boldsymbol{v} boldsymbol{m} / boldsymbol{s} ) w.r.t. trolley in the backward direction. If the length of the trolley is ( mathrm{L} ), then the displacement of the man with respect to earth, measured as a function of time, will attain a maximum value of A ( cdot frac{4}{3} L ) B. ( frac{2}{3} L ) c. ( frac{5 L}{3} ) D. ( 1.5 L ) | 11 |

306 | 22 locities v, and 18. In Fig. 6.307, blocks A and B move with velocities V2 along horizontal direction. Find the ratio of y.lv W Fig. 6.307 sine, a sin cos 82 sin e sine, cose, cos cos | 11 |

307 | A coin is tossed with a velocity of ( 3 mathrm{m} / mathrm{s} ) at A. a) What happens to the velocity along AB, along DE and at C? b) What happens to the acceleration of the coin along ( A C ) and ( C E ? ) c) What is the distance and vertical displacement covered by the coin between A and E. | 11 |

308 | 49. A plane flying horizontally at 100 ms releases an object which reaches the ground in 10 s. At what angle with horizontal it hits the ground? a. 550 b. 45o c. 60° d. 75° | 11 |

309 | 13. A truck is moving with a constant velocity of 34 km In which direction (angle with the direction of motion of truck) should a stone be projected up with a velocity 20 ms, from the floor of the truck, so as to appear at right angles to the truck, for a person standing on earth? a. cos b. Cos -1 a. cost ( 22 COS d. cost (2) | 11 |

310 | Which of the following cannot be in equilibrium? A. ( 10 N, 10 N, 5 N ) ( N ) B. ( 5 N, 7 N, 9 N ) c. ( 8 N, 4 N, 13 N ) D. ( 9 N, 6 N, 5 N ) | 11 |

311 | Two particles ( A ) and ( B ) are placed as shown in figure. The particle A on the top of a tower of height H is projected horizontally with a velocity u and the particle B is projected along the horizontal surface towards the foot of the tower, simultaneously. When particle A reaches at ground, it simultaneously hits particle B. Then the speed of projected particle B is:(neglect any type of friction) A ( cdot d sqrt{frac{g}{2 H}} ) B. ( d sqrt{frac{g}{2 H}}-u ) ( c ) [ sqrt[d]{frac{g}{2 H}+u} ] D. | 11 |

312 | Consider a plane flying due West at 200 MPH. The co-pilot is firing a gun in the opposite direction the plane is flying due East. If the co-pilot clocks the bullets at ( 500 mathrm{MPH} ), how fast would the bullets be clocked from the ground? A. 300 MPH East в. 700 МРн Еазн c. 500 MPH West D. 200 MPH West E. cannot determine with information provided | 11 |

313 | Ideal fluid flows along a flat tube of constant cross-section, located in a horizontal plane and bent as shown in figure above (top view). The flow is steady. Are the velocities of the fluid equal at points 1 and ( 2 ? ) A. Velocity at point 1 is less than velocity at point 2 B. Velocity at point 1 is more than velocity at point 2 c. velocity at point 1 is equal to velocity at point 2 D. can’t be determined | 11 |

314 | 35. Maximum height attained from the point of projection a. 1.25 m b. 12.5 m c. 2.25 m d. None of these | 11 |

315 | A car accelerates on a horizontal road due to the force exerted by A. The engine of the car B. The driver of the car c. The car on earth D. The road on the car | 11 |

316 | w (0) b 46′ ton 60. A projectile is given an initial velocity of i +2j. The cartesian equation of its path is (g = 10 ms?). a. y = 2x – 5.r b. y = x – 5×2 c. 4y = 2x – 5×2 d. y = 2x – 25/? | 11 |

317 | The angle turned by a body undergoing circular motion depends on time as ( boldsymbol{theta}=boldsymbol{theta}_{0}+boldsymbol{theta}_{1} boldsymbol{t}+boldsymbol{theta}_{2} boldsymbol{t}^{2} . ) Then the angular acceleration of the body is ( A cdot theta_{1} ) в. ( theta_{2} ) ( c cdot 2 theta_{1} ) D. ( 2 theta_{2} ) | 11 |

318 | A particle projected from 0 and moving freely under gravity strikes the horizontal plane passing through 0 at a distance ( R ) from the starting point 0 as shown in the figure. Then This question has multiple correct options A. there will be two angles of projection if ( R g<u^{2} ) B. the two possible angles of projection are complementary c. the product of the possible times of flight from 0 to ( A ) is ( frac{2 R}{g} ) D. there will be more than two angles of projection if ( R g=u^{2} ) | 11 |

319 | Two particles having position vectors ( vec{r}_{1}=3 hat{i}+5 hat{j} mathrm{m} ) and ( vec{r}_{2}=-5 hat{i}+3 hat{j} mathrm{m} ) are moving with velocities ( vec{V}_{1}=4 hat{i}+ ) ( 3 hat{j} mathrm{m} / mathrm{s} ) and ( vec{V}_{2}=-a hat{i}+4 hat{j} mathrm{m} / mathrm{s} . ) If they collide after 2 seconds, the value of ( a ) is: A . -2 B. -4 ( c .-6 ) D. -8 | 11 |

320 | Two vectors ( overrightarrow{boldsymbol{A}}=mathbf{2} hat{mathbf{i}}+hat{boldsymbol{j}} ) and ( overrightarrow{boldsymbol{B}}=boldsymbol{a} hat{boldsymbol{i}}- ) ( 2 hat{j} ) are perpendicular to each other. The value of a is A. B. 2 ( c cdot 3 ) D. 4 | 11 |

321 | A particle is projected from the ground with an initial velocity of ( 20 mathrm{m} / mathrm{s} ) at an angle of ( 30^{circ} ) with horizontal. The magnitude of change in velocity in a time interval from ( t=0 ) to ( t=0.5 mathrm{s} ) is ( left(g=10 m / s^{2}right) ) ( A cdot 5 mathrm{m} / mathrm{s} ) в. ( 2.5 mathrm{m} / mathrm{s} ) ( c cdot 2 m / s ) D. ( 4 mathrm{m} / mathrm{s} ) | 11 |

322 | The path of projectile is represented by ( boldsymbol{y}=boldsymbol{P} boldsymbol{x}-boldsymbol{Q} boldsymbol{x}^{2} ) begin{tabular}{|l|l|l|l|} hline multicolumn{2}{|c|} { Column I } & multicolumn{2}{|c|} { Column II } \ hline i. & Range & a. & ( P / Q ) \ hline ii. & Maximum height & b. & ( P ) \ hline iii. & Time of flight & c. & ( P^{2} / 4 Q ) \ hline iv. & Tangent of angle of projection is & d. & ( sqrt{frac{2}{Q g}} ) P \ hline end{tabular} | 11 |

323 | Their common speed ( mathbf{v} ) will be ( mathbf{A} cdot frac{q}{4} sqrt{frac{1}{m R pi varepsilon_{0}}} ) ( mathbf{B} cdot q sqrt{frac{m R pi varepsilon_{0}}{4}} ) ( mathbf{c} cdot 4 q sqrt{m R pi varepsilon_{0}} ) D. ( frac{4 q}{sqrt{m R pi varepsilon_{0}}} ) | 11 |

324 | Assertion It is possible to accelerate even if you are travelling at constant speed. Reason In the uniform circular motion, even if the particle has the constant speed, it has an acceleration. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

325 | Write a vector in the direction of the vector ( hat{boldsymbol{i}}-boldsymbol{2} hat{boldsymbol{j}}+2 hat{boldsymbol{k}} ) that has magnitude 9 units. | 11 |

326 | The graph shows position as a function of time for two trains ( A ) and ( B ) running on parallel tracks. For times greater than ( t=0, ) which of the following statement is true? A. At time ( t_{B} ), both trains have the same velocity B. Both trains speed up all the time ( c . ) Both trains may have the same velocity at some time earlier than ( t_{B} ) D. Graph indicates that both trains have the same acceleration at a give | 11 |

327 | A car is travelling with an acceleration of ( 2 m / s^{2} . ) If the diameter of the car wheel is ( 50 mathrm{cm}, ) the angular acceleration of the wheel is: A ( .2 .5 mathrm{rad} / mathrm{s}^{2} ) B. 8 rad/s( ^{2} ) C ( .5 mathrm{rad} / mathrm{s}^{2} ) D. 4 rad/s( ^{2} ) | 11 |

328 | 12. A stone is projected from level ground such that its horizontal and vertical components of initial velocity are u = 10 m/s and u, = 20 m/s respectively. Then the angle between velocity vector of stone one second before and one second after it attains maximum height is: (a) 30° (b) 45° (c) 60° (d) 90° | 11 |

329 | A ferris wheel with a radius of ( 8.0 m ) makes 1 revolution every 10 s.When a passenger is at the top essentially a diameter above the ground, he releases a ball. How far from the point on the ground directly under the release point does the ball land? ( mathbf{A} cdot mathbf{0} ) в. ( 1.0 mathrm{m} ) ( c .8 .0 m ) D. ( 9.1 mathrm{m} ) | 11 |

330 | 58. The speed of a projectile at its maximum height times its initial speed. If the range of the projectile is pl times the maximum height attained by it, P is equal to a. 4/3 b. 2√3 c. 4√3 d. 3/4 | 11 |

331 | Two forces simultaneously act on a particle making an angle ( 120^{circ} ) with each other if one of them is reversed the acceleration of the particle becomes ( sqrt{3} ) times its initial value. The ratio of the magnitude of the forces is? A . 1: 2 B. 1: 1 ( c cdot 2: 1 ) D. 1: 3 | 11 |

332 | A man throws a ball at height of ( 10 mathrm{m} ) at an angle of ( 35^{circ} ) from horizontal. If mass of ball is ( 0.5 mathrm{kg} ) and its initial speed is ( 30 mathrm{m} / mathrm{s} ) ( boldsymbol{g}=-mathbf{9 . 8} frac{boldsymbol{m}}{s^{2}} ) How long is the ball in the air? A . ( 2.26 s ) B. 4.02s ( c cdot 1.76 s ) D. 5.05s E. 1.12 s | 11 |

333 | Uniform Circular Motion refers to a motion of an object in a circle at a constant A. Velocity B. Speed c. Both D. None | 11 |

334 | A particle is projected at an angle of ( 45^{circ} ) from ( 8 m ) before the foot of a wall,just touches the top of the wall and falls on the ground on the opposite side at a distance ( 4 m ) from it. The height of wall is: A ( frac{2}{3} m ) в. ( frac{4}{3} m ) c. ( frac{8}{3} m ) D. ( frac{3}{4} m ) | 11 |

335 | Two particles are projected in air with speed ( u ) at angles ( theta_{1} ) and ( theta_{2} ) (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then which one of the following is correct? (where ( T_{1} ) and ( T_{2} ) are the time of flight.) A. ( theta_{1}>theta_{2} ) a B ( cdot theta_{1}=theta_{2} ) c. ( T_{1}<T_{2} ) D. ( T_{1}=T_{2} ) | 11 |

336 | The position vector of a particle changes with time according to the relation ( vec{r}(t)=15 t^{2} hat{i}+left(4-20 t^{2}right) hat{j} ) What is the magnitude of the acceleration at ( t=1 ? ) A . 40 в. 100 c. 25 D. 50 | 11 |

337 | Ship A is travelling with a velocity of 5 kmh due east. A second ship is heading 30° east of north. What should be the speed of second ship if it is to remain always due north with respect to the first ship? 10 km h-b. 9 km h c. 8 kmh d. 7 kmh La | 11 |

338 | A bus is moving on a straight road towards North with a uniform speed of ( mathbf{5 0} mathrm{km} / mathrm{h} . ) If the speed remains unchanged after turning through ( 90^{circ} ) the increase in the velocity of the bus in the turning process is? | 11 |

339 | 12 13 63. In the arrangement show of B is ā, then fin ngement shown in Fig. 6.335, if the acceleration is a. then find the acceleration of A. Fixed incline Fig. 6.335 a. a sin a b. a cote c. a tan o d. a(sin a cot 0 + cos a) | 11 |

340 | A particle moves along +x-axis with initial velocity ( 5 mathrm{m} / mathrm{s} ). If acceleration (a) varies with time (t) as shown in a-tt graph, then the velocity of the particle just after 4 second is A ( .2 .5 m / s ) B. ( 10 mathrm{m} / mathrm{s} ) c. ( -1.25 m / s ) D. ( -5 m / s ) | 11 |

341 | 5.3 20. A motor boat is to reach at a point 30° upstream on the other side of a river 120 flowing with velocity 5 ms. The velocity of motor boat with respect to water is 5 1/3 ms. The driver should Fig. A.10 steer the boat at an angle a. 30° w.rt. the line of destination from the starting point b. 60° w.r.t. normal to the bank c. 120°w.rt. stream direction d. None of these | 11 |

342 | A police van moving on a highway with a speed of ( 30 mathrm{km} h^{-1} ) fires a bullet at a thief’s car speeding away in the same direction with a speed of ( 192 mathrm{km} h^{-1} . ) If the muzzle speed of the bullet is 150 ( mathrm{m} s^{-1}, ) with what speed does the bullet hit the thief’s car? ( mathbf{A} cdot 95 mathrm{m} mathrm{s}^{-1} ) B . ( 105 mathrm{m} s^{-1} ) C. ( 115 mathrm{m} s^{-1} ) D. ( 125 mathrm{m} s^{-1} ) | 11 |

343 | In uniform circular motion the particle moves with a A. Constant speed B. Variable speed c. constant acceleration D. Variable acceleration | 11 |

344 | 30. A ball rolls off the top of a stairway horizontally with a velocity of 4.5 ms. Each step is 0.2 m high and 0.3 m wide. If g is 10 ms?, and the ball strikes the edge of nth step, then n is equal to a. 9 b. 10 c. 11 d. 12. | 11 |

345 | Minimum number of unequal vectors which can give zero resultant are: A . two B. three c. four D. more than four | 11 |

346 | Tyres are made circular because: A. they can be inflated B. they require less materaial C. they look beautiful D. they face less friction | 11 |

347 | toppr Q Type your question- a. The angle between the edge along the ( z ) -axis (line ab) and the diagonal from the origin to the opposite corner (line ad). b. The angle between line ( a c ) (the diagonal of a face) and line ( a d ) A ( cdot ) a. ( cos ^{-1} frac{1}{sqrt{2}} ) b. ( cos ^{-1} frac{sqrt{2}}{sqrt{3}} ) B. a. ( cos ^{-1} frac{1}{sqrt{3}} ) c. a ( cos ^{-1} frac{1}{sqrt{3}} ) b. ( cos ^{-1} frac{sqrt{3}}{sqrt{3}} ) D. a. ( cos ^{-1} frac{2}{sqrt{3}} ) | 11 |

348 | A car traveling at a constant speed of ( 30 m / s ) passes a highway patrol car, which is at rest. The police officer accelerates at a constant rate of ( 3 m / s^{2} ) and maintains this rate of acceleration until he pulls next to the speeding car. Assume that the police car starts to move at the moment the speeder passes the police car. What is the time required for the police officer to catch the speeder? ( mathbf{A} cdot 20 s ) B. ( 30 s ) c. ( 40 s ) D. ( 50 s ) | 11 |

349 | 30. A hose lying on the ground shoots a stream of water upward at an angle of 60° to the horizontal with the velocity of 16 ms. The height at which the water strikes the wall 8 m away is a. 8.9 m b. 10.9 m c. 12.9 m d. 6.9 m 1.1 ppiootile is at | 11 |

350 | In Fig. the angle of inclination of the inclined plane is ( 30^{0} . ) Find the horizonta velocity ( V_{0} ) so that the particle hits the inclined plane perpendicularly. A ( cdot V_{0}=sqrt{frac{2 g H}{5}} ) B. ( V_{0}=sqrt{frac{2 g H}{7}} ) ( mathbf{c} cdot_{V_{0}}=sqrt{frac{g H}{5}} ) D ( cdot V_{0}=sqrt{frac{g H}{7}} ) | 11 |

351 | A body is revolving with a constant speed along a circular path. If the direction of its velocity is reserved, keeping speed unchanged, then at that instant. A. centripetal force disappears B. centripetal force will be doubled C. the centripetal force does not suffer any change in magnitude and direction both D. the centripetal force does not suffer any change in magnitude but its direction is reserved. | 11 |

352 | 18. Minimum separation between A and B is a. 3 m b. 6 m c. 12 m d. 9 m | 11 |

353 | Illustration 5.73 A stone tied to an inextensible string of length 7 = 1 m is kept horizontal. If it is released, find the angular speed of the stone when the string makes an angle O= 30° with horizontal. | 11 |

354 | shows a rod of length I resting on a wall and the floor. Its lower end A is pulled towards left with a constant velocity ( v ) Find the velocity of the other end ( B ) downward when the rod makes an angle ( theta ) with horizontal. | 11 |

355 | When a body moves in a circular motion A. its direction constantly changes B. its direction remains constant C. its velocity vector is always perpendicular to the direction D. all of the above | 11 |

356 | TUNC U UDU 14. Find the resultant of three vectors OA. OB and OC show in the following figure. Radius of the circle is R. C 450 45o (a) 2R (c) RZ (b) R(1+2) (d) R(12 – 1) | 11 |

357 | An open topped freight car of mass ( mathbf{1 0}, mathbf{0 0 0} boldsymbol{k g} ) is coasting without friction along a level track in heavy rains, falling vertically downwards. Initially the car is empty and is moving with a velocity of ( 0.88 m / s . ) What is the velocity of the car after it has collected 1000 kg of water? | 11 |

358 | The tire pictured below is rolling to the left at a constant speed without slipping on a horizontal roadway. What is the direction of the acceleration of the part of the tire that is in contact with the road? A. Left B. Right c. up D. Down E. The acceleration of this part of the tire is zero | 11 |

359 | Two particles move on a circular path (one just inside and the other just outside) with angular velocities ( omega ) and ( 5 omega ) starting from the same point. Then: This question has multiple correct options A cdot they cross each other at regular intervals of time ( frac{pi}{2 omega} ) when their angular velocities are directed opposite to each other B. they cross each other at points on the path subtending an angle of ( 60^{circ} ) at the centre if their angular velocities are directed opposite to each other C . they cross at intervals of time ( frac{pi}{3 omega} ) if their angular velocities are directed opposite to each other D. they cross each other at points on the path subtending ( 90^{circ} ) at the centre if their angular velocities are similar to each other | 11 |

360 | A man is ( 45 mathrm{m} ) behind the bus when the bus start accelerating from rest with acceleration 2.5. With what minimum velocity should the man start running to catch the bus A . 12 B . 14 c. 15 D. 16 | 11 |

361 | A system is shown in the figure. A man a standing on the block is pulling the rope. Velocity of the point of string in contact with the hand of the man is ( 2 m / s ) downwards. The velocity of the block will be: [Assume that the block does not rotate ( ] ) A. ( 3 m / s ) B. ( 2 m / s ) c. ( frac{1}{2} m / s ) D. ( 1 mathrm{m} / mathrm{s} ) | 11 |

362 | 2 8 Vo V2 8 26. In Fig. A. 11, the angle of inclination of the inclined plane is 30°. Find the horizontal velocity Vo so that the particle hits the inclined plane perpendicularly. |2gH 7 9030° Fig. A.11 /23H a. V b. Vo = 7 c. Vo = 1/3 d. Vo = 18H | 11 |

363 | 42. At a height 0.4 m from the ground, the velocity of a projectile in vector form is v = (6i +2j) ms. The angle of projection is a. 45° b. 60° c . 30° d. tan (3/4) Amanin tile in than in the word direction making an | 11 |

364 | A fan is running at 3000 rpm. It is switched off. It comes to rest by uniformly decreasing its angular speed in 10 seconds. The total number of revolutions in this period. A. 150 B. 250 c. 350 D. 300 | 11 |

365 | If an object is thrown vertically up, with the initial speed ( u ) from the ground, then the time taken by the object to return back to the ground is ( ^{mathrm{A}} cdot frac{u^{2}}{2 g} ) в. ( frac{u^{2}}{g} ) c. ( frac{u}{2 g g} ) D. ( frac{2 u}{g} ) | 11 |

366 | A force of ( 10 mathrm{N} ) is resolved into the perpendicular components. If the first component makes ( 30^{0} ) with the force the magnitudes of the components are: A . 5N, 5N B . ( 5 sqrt{2} mathrm{N}, ) 5N ( mathbf{c} cdot 5 sqrt{3} mathbf{N}, 5 mathrm{N} ) D. ( 10 mathrm{N}, 1 sqrt{3} mathrm{N} ) | 11 |

367 | When in going east at ( 10 mathrm{km} / mathrm{h} ) a train moving with constant velocity appears to be moving exactly north – east. when my velocity is increased to ( 30 mathrm{km} / mathrm{h} ) east it appears to be moving north What is the velocity of train along north (in ( mathrm{Kmph}) ) ? ( A cdot 30 mathrm{km} / mathrm{h} ) B. 20 km/h ( c cdot 50 mathrm{km} / mathrm{h} ) D. ( 10 mathrm{km} / mathrm{h} ) | 11 |

368 | The velocity of the body at any instant is A ( cdot frac{M+2 N t^{4}}{4} ) B. 2N c. ( frac{M+2 N}{4} ) D. ( 2 N t^{3} ) | 11 |

369 | 6. The time in which the ball strikes the floor of elevator is given by a. 2.13s b. 4.26 S c. 1.0 s d. 2.0 s L L – ched by the ball am | 11 |

370 | A particle moves in a straight line and its speed depends on time as ( boldsymbol{v}=mid mathbf{2 t}- ) 3). Find the displacement of the particle in ( 5 s ) | 11 |

371 | 18-10 31. A machine gun is mounted on the top of a tower of heghe h. At what angle should the gun be inclined to cover a maximum range of firing on the ground below? The muzzle speed of bullet is 150 ms. Take g = 10 ms? | 11 |

372 | acceleration 13. Measuring g The figure shows a method for measuring the acceler due to gravity. The ball is projected upward by a 4 The ball passes electronic “gates” 1 and 2 as it rises again as it falls. Each gate is connected to a sep: timer. The first passage of the ball through each gate starts the corresponding timer, and the second passage through the same gate stops the timer. The time intervals At, and At, are thus measured. The vertical distance between the two gates is d. If d = 5 m, At, = 3 s, At,= 2 s, find the measured value of acceleration due to gravity (in ms). Gate 2 B: 1:18 0000 0 Timer 2 Te TEL:5:1:1:13 0000 Timer 1 Bal Gun Fig. A.49 14 A lomotion of | 11 |

373 | Consider the following statements A and B given below and identity the correct answer. A) With the help of the relative velocity of rain with respect to man, the direction of the umbrella held by him to save from the rain is determined. B) A parallelogram has sides represented by vectors ( vec{a} ) and ( overrightarrow{mathrm{b}} ). If ( overrightarrow{mathrm{d}}_{1} ) and ( overrightarrow{mathrm{d}}_{2} ) are the diagonal vectors of the parallelogram then ( 2left(mathrm{a}^{2}+mathrm{b}^{2}right)=mathrm{d}_{1}^{2}+mathrm{d}_{2}^{2} ) A. Both A and B are true B. A is true but B is false c. ( B ) is true but ( A ) is false D. Both A and B are false | 11 |

374 | Any vector in an arbitrary direction can always be replaced by two (or three): A. Parallel vectors which have the original vector as their resultant B. Mutually perpendicular vectors which have the original vector as their resultant c. Arbitrary vectors which have the original vector as their resultant D. It is not possible to resolve a vector | 11 |

375 | 9. On a two-lane road, car A is travelling with a speed of 36 kmh. Two cars B and C approach car A in opposite directions with a speed of 54 kmh each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident? | 11 |

376 | d. non-zero UUM 13. From the top of a tower of height 200 m, a ball A: projected up with speed 10 ms and 2 s later, ano ball B is projected vertically down with the same speed Then a. Both A and B will reach the ground simultaneously b. Ball A will hit the ground 2 s later than B hitting the ground c. Both the balls will hit the ground with the same velocity d. Both will rebound to the same height from the ground. if both have same coefficient of restitution. nale – 200 with 1 | 11 |

377 | A particles revolves along a circle with a uniform speed. The motion of the particle is A. one dimensional B. two dimensional. c. translatory D. oscillatory | 11 |

378 | If ( A ) is to the south of ( B ) and ( C ) is to the east of ( mathrm{B} ), in what direction is ( mathrm{A} ) with respect to C? A. North-east B. North-west c. South-west D. None of the above | 11 |

379 | A force ( overrightarrow{boldsymbol{F}}=2 hat{boldsymbol{i}}-boldsymbol{3} hat{boldsymbol{k}} ) acts on a particle at ( vec{r}=0.5 hat{j}-2 hat{k} . ) The torque ( vec{Gamma} ) acting on the particle relative to a point with co-ordinates ( (2.0 mathrm{m}, 0 ;-3.0 mathrm{m}) ) is? | 11 |

380 | Consider driving in a car at 65 MPH while drinking a cup of coffee. Which of the following would be traveling at the greatest speed? A. The car, coffee and you are traveling at the same velocity B. The coffee is traveling with the greatest velocity assuming it has the least mass c. The car is the only object with velocity, as the other objects are within the car D. None of the objects have velocity, as they are all traveling together E. As velocity is a function of speed and direction, this question cannot be answered | 11 |

381 | In a situation, a board is moving with a velocity ( v ) with respect to earth, while a man A and man B are running with a velocity ( 2 v ) with respect to earth and both men are running from the opposite ends of the board at the same time, as shown. Length of the board is ( L ). If they meet after time ( boldsymbol{T}, ) then This question has multiple correct options A. value of ( mathrm{T} ) is ( mathrm{L} / 4 mathrm{v} ) B. value of ( T ) is ( L / 2 v ) C. Displacement of man B with respect to board in time ( T ) is ( 3 L / 4 ) D. Displacement of man A with respect to board in time ( T ) is L/4 | 11 |

382 | A particle starts travelling on a circle with constant tangential acceleration. The angle between velocity vector and acceleration vector, at the moment when particle complete half the circular track, is: ( mathbf{A} cdot tan ^{-1}(2 pi) ) B. ( tan ^{-1}(pi) ) ( mathbf{c} cdot tan ^{-1}(3 pi) ) D. ( tan ^{-1}(2) ) | 11 |

383 | Two particle ( A ) and ( B ) are located in ( x-y ) plane at points (0,0) and ( (0,4 mathrm{m}) ). They simultaneously start moving with velocities. ( vec{V}_{A}=2 hat{j} m / s ) and ( vec{V}_{B}= ) 2 ì ( m / s . ) Select the correct alternative(s). This question has multiple correct options A. The distance between them is constant B. The distance between them first decreases and then increases c. The shortest distance between them is ( 2 sqrt{2} m ) D. Time after which they are at minimum distance is 1 s | 11 |

384 | Find a vector in thedirection of ( 5 hat{i}-widehat{j}+ ) ( 2 widehat{k} ) which has magnitude 8 units. A ( cdot frac{8}{sqrt{30}} hat{i}-frac{40}{sqrt{30}} hat{j}+frac{16}{sqrt{30}} widehat{k} ) B. ( frac{16}{sqrt{30}} hat{i}+frac{8}{sqrt{30}} hat{j}-frac{40}{sqrt{30}} widehat{k} ) c. ( frac{40}{sqrt{30}} hat{i}-frac{8}{sqrt{30}} hat{j}+frac{16}{sqrt{30}} widehat{k} ) D. None | 11 |

385 | Illustration 5.1 At what point on a projectile’s trajectory, its speed is minimum? If a stone is thrown with a speed vo at an angle @ with horizontal, find the velocity of the stone when its line of motion makes an angle with horizontal. | 11 |

386 | Which of the following statement is correct A. The motion of earth around the sun is vibratory B. The motion of a mosquito in a room is in a straight line C. The motion of moon around the earth is periodic D. None of these | 11 |

387 | le 0 above 55. A projectile is fired from level ground at an angle o the horizontal. The elevation angle Pof the higher seen from the launch point is related to O by the a. tan o = 2 tano b. tano = tano highest pointas e by the relation c. tan d. tan o = -tan = -tan e | 11 |

388 | Air resistance is proportional to This question has multiple correct options A ( . v ) B ( cdot v^{2} ) ( c cdot v^{-2} ) ( mathbf{D} cdot v^{3} ) | 11 |

389 | A swimmer swims in still water at a speed ( =5 k m / h r . ) He enters a ( 200 m ) wide river, having river flow speed ( =4 k m / h r ) at a point ( A ) and proceeds to swim at an angle of ( 127^{0}left(sin 37^{*}-0.6right) ) with the river flow direction. Another point B is located directly across ( A ) on the other side. The swimmer lands on the river bank at a point C. from which he walks the distance ( mathrm{CB} ) with a speed ( =3 k m / h r ) The total time in which he reach from ( mathbf{A} ) to B is ( mathbf{A} cdot 5 min ) B. 4 min c. 3 min D. None | 11 |

390 | The displacement ( (x) ) of a particle starting from rest is given by ( boldsymbol{x}=mathbf{6} boldsymbol{t}^{2}- ) ( t^{3} . ) The time at which the particle will attain zero velocity again is A . 2 B. 4 ( c .6 ) D. | 11 |

391 | 36. A ball is thrown at different angles with the same speed u and from the same point and it has the same range in both the cases. If y, and y2 are the heights attained in the two cases, then yı + y2 is equal to – 2u² a. – D. 8 c. 28 . 48 02 b. | 11 |

392 | A particle ( A ) moves along a circle of radius ( R=50 mathrm{cm} ) so that its radius vector ( r ) relative to the point ( O ) (figure) rotates with the constant angular velocity ( omega=0.40 ) rad ( / ) s. Then magnitude of the velocity of the particle, and the magnitude of its total acceleration will be A ( cdot v=0.4 mathrm{m} / mathrm{s}, a=0.4 mathrm{m} / mathrm{s}^{2} ) B . ( v=0.32 mathrm{m} / mathrm{s}, a=0.32 mathrm{m} / mathrm{s}^{2} ) C ( cdot v=0.32 mathrm{m} / mathrm{s}, a=0.4 mathrm{m} / mathrm{s}^{2} ) D. ( v=0.4 mathrm{m} / mathrm{s}, a=0.32 mathrm{m} / mathrm{s}^{2} ) | 11 |

393 | The angle turned by a body undergoing circular motion depends on time as ( boldsymbol{theta}=sqrt{mathbf{2}} boldsymbol{theta}_{0}+mathbf{3} boldsymbol{theta}_{1} boldsymbol{t}+boldsymbol{theta}_{2} boldsymbol{t}^{2} ) Then the angular acceleration of the body is A. ( sqrt{theta_{1}} ) в. ( sqrt{3} theta_{2} ) ( c cdot 2 theta_{1} ) D. ( 2 theta_{2} ) | 11 |

394 | 21. The point from where a ball is projected is taken as the origin of the coordinate axes. The x and y components of its displacement are given by x = 6t and y = 8t -57. Wha is the velocity of projection? a. 6 ms-1 b. 8 ms -1 c. 10 ms- d. 14 ms -1 | 11 |

395 | 9. An airplane is observed by two observers traveling 60 kmh ‘ in two vehicles moving in opposite direction on a straight road. To an observer in one vehicle, the plane appears to cross the road track at right angles while to the other appears to be 45º. At what angle does the plane actually cross the road track and what is its speed relative to ground? | 11 |

396 | A ball (solid sphere) of mass ( m ) is rolling on a smooth horizontal surface as shown in figure. At an instant the magnitude of the velocity of the centre of mass is ( v_{0} ) and its angular velocity is ( omega frac{v_{0}}{2 R}, ) where ( R ) is the radius of the ball. The total kinetic energy of the rolling ball at this instant is:- ( mathbf{A} cdot frac{7}{5} m R^{2} omega_{0}^{2} ) B. ( frac{11}{5} m R^{2} omega_{0}^{2} ) ( c ) D. | 11 |

397 | A girl riding a bicycle with a speed of 5 ( m s^{-1} ) towards north direction, observes rain falling vertically down. If she increases her speed to ( 10 mathrm{ms}^{-1}, ) rain appears to meet her at ( 45^{circ} ) to the vertical. What is the speed of the rain? A ( cdot 5 sqrt{2} mathrm{ms}^{-1} ) B. ( 5 m s^{-1} ) D. ( 10 m s^{-1} ) | 11 |

398 | In the given figure, ( a=15 mathrm{m} / mathrm{s}^{2} ) represents the total acceleration of a particle moving in the clockwise direction in a circle of radius ( boldsymbol{R}=mathbf{2 . 5 m} ) at a given instant of time. The speed of the particle is: ( mathbf{A} cdot 6.2 m / s ) B. ( 4.5 m / s ) ( c .5 .0 m / s ) D. ( 5.7 m / s ) | 11 |

399 | 56. A projectile has initially the same horizontal veloci as it would acquire if it had moved from rest with unif acceleration of 3 ms for 0.5 min. If the maximum heich reached by it is 80 m, then the angle of projection i (8 = 10 ms2) a. tan-3 b. tan-‘(3/2) c. tan-(4/9) d. sin-(4/9) | 11 |

400 | Two wheels are constructed, as shown in Figure, with four spokes. The wheels are mounted one behind the other so that an observer normally sees a total of eight spokes but only four spokes are seen when they happen to align with one another. If one wheel spins at 6 rev/min, while other spins at 8 rev/min in same sense, how often does the observer see only four spokes? A. 4 times a minute B. 6 times a minute c. 8 times a minute D. Once in a minute | 11 |

401 | Assertion To move a body uniformly in a circular path, an external agent has to apply a force. Reason To more a body uniformly in a circular path, an external agent has to do work. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect and Reason is correct | 11 |

402 | If you are traveling on a spaceship close to the speed of light (pick a number e.g. 0.95c), With or without constant acceleration whichever works for the question. Time will slow down relative to earth and you will be able to travel a greater distance than you would be able to without relativistic effects. You would also be able to return to earth with significant time passed relative to your experience. My question is, what would it feel like on the spaceship…I know the standard answer is you wouldn’t feel anything, but logically, if you were traveling through galaxy after galaxy in a relativistic time of human life then intuition says everything would look like it whizzing past. Basically, what is the human experience of being able to trave interstellar distances? | 11 |

403 | The adjacent sides of a paralleleogram ( operatorname{are} vec{A}=2 hat{i}-3 hat{j}+hat{k} quad ) and ( quad vec{B}= ) ( -2 hat{i}+4 hat{j}-hat{k} ) What is the area of the parallelogram? A. 4 units B. 7units c. ( sqrt{5} ) units D. ( sqrt{8} ) units | 11 |

404 | single Correct Answer Type f a stone has to hit at a point which is at a distance ( d ) away and at a height ( h ) above the point from where the stone starts, then what is the value of initial speed ( u ) if the stone is thrown at an angle ( theta ? ) A ( cdot frac{g}{cos theta} sqrt{frac{d}{(2(d tan theta-h)}} ) в. ( frac{d}{cos theta} sqrt{frac{g}{(2(d tan theta-h)}} ) c. ( sqrt{frac{g d^{2}}{h cos ^{2} theta}} ) D. ( sqrt{frac{g d^{2}}{(d-h)}} ) | 11 |

405 | A particle starts moving from point ( (2, ) 10,1)( . ) Displacement for the particle is 8 ( hat{mathbf{i}}-2 hat{mathbf{j}}+hat{boldsymbol{k}} . ) The final coordinates of the particle is A. (10,8,2) ) в. (8,10,2) ( c cdot(2,10,8) ) D. (8,2,10) | 11 |

406 | When the particle reaches its maximum height, which of the following MUST be true about the particle? A. It has the same horizontal speed it had initially B. It has the same vertical speed it had initially C. Its net acceleration is momentarily zero D. It is momentarily at rest E. All of the above | 11 |

407 | How can you say circular motion of an object is said to be an accelerated motion. | 11 |

408 | 4. A ladder is resting with the wall at an angle of 30°. A man is ascending the ladder at the rate of 3 ft/sec. His rate of approaching the wall is (a) 3 ft/sec (b) ft/sec (d) ft/sec ft sec | 11 |

409 | MAPOCIUIU MULUI VOL From the top of tower of height 80 m, two stones are projected horizontally with velocities 20 ms and 30 ms” in opposite directions. Find the distance between both the stones on reaching the ground in 10 m). | 11 |

410 | A steamer plies between two stations ( boldsymbol{A} ) and ( B ) on opposite banks of a river, always following the path ( A B ). The distance between stations ( A ) and ( B ) is 1200 ( m ). The velocity of the current is ( sqrt{17} m s^{-1} ) and is constant over the maim width of the river. The line ( A B ) makes an angle ( 60^{circ} ) with the direction of the flow. The steamer takes 5 min to cover the distance ( A B ) and back. a. Find the velocity of steamer with respect to water. b In what direction should the steamer move with respect to line ( boldsymbol{A B} ) ? | 11 |

411 | O 0510 COOL 11. A ball is fired from point P, with an initial speed of 50 ms at an angle of 53°, with the horizontal. At the same time, a long wall AB at 200 m from point P starts moving toward P with a constant speed of 10 ms. Find 50 ms-1 S P53° 200 m Fig. 5.190 a. the time when the ball collides with wall AB. b. the coordinate of point C, where the ball collides, taking point P as origin. | 11 |

412 | particle is projected with a certain velocity at an angle a hove the horizontal from the foot of an inclined plane of inclination 30°. If the particle strikes the plane normally, then a is equal to a. 30° + tan-1 b. 45° c. 60° d. 30° + tan-|(273) | 11 |

413 | Given that ( overrightarrow{boldsymbol{A}}+overrightarrow{boldsymbol{B}}=overrightarrow{boldsymbol{C}} ). If ( |overrightarrow{boldsymbol{A}}|=4,|overrightarrow{boldsymbol{B}}|= ) ( mathbf{5} ) and ( |overrightarrow{boldsymbol{C}}|=sqrt{mathbf{6 1}}, ) the angle between ( boldsymbol{A} ) and ( B ) is A ( .30^{circ} ) B. ( 60^{circ} ) ( c .90^{circ} ) D. ( 120^{circ} ) | 11 |

414 | 44. Two guns on a battleship simultaneously fire two shells with same speed at enemy ships. ie Battleship If the shells follow the parabolic A trajectories as shown in Fig. A.22, Fig. A.22 which ship will get hit first? a. A b. B c. both at same time d. need more information | 11 |

415 | 43. A projectile is thrown in the upward direction making an angle of 60° with the horizontal direction with a velocity of 150 ms. Then the time after which its inclination with the horizontal is 45° is a. 15(13 – 1)s b. 15673 +1) s c. 7.56√3-1)s d. 7.56√3+1)s c ania | 11 |

416 | A car is moving with speed 30 m/sec on a circular path of radius 500 m. Its speed is increasing at the rate of ( 2 m / s e c^{2} . ) What is the acceleration of the car at that moment? | 11 |

417 | To get from one office to another, one travels as follows (with all angles measured clockwise from the West) ( 2 m ) at ( 180^{circ}, 0.5 m ) at ( 150^{circ}, ) and ( 1 m ) at ( 30^{circ} ) How far will a person be from his starting point? ( (text { in } m) ) A . 1.5 B. 1.43 ( c .1 ) D. 1.96 | 11 |

418 | A body is moving with a constant speed ( v ) in a circle of radius ( r . ) Its angular acceleration is: A . ( v r ) B. ( frac{v}{r} ) c. zero D. ( v r^{2} ) | 11 |

419 | Illustration 5.6 The horizontal range of a projectile is 23 times its maximum height. Find the angle of projection. friention and | 11 |

420 | The co-ordinates of a moving particle at any time ( t ) are given by ( alpha t^{3} ) and ( y=beta t^{3} ) The speed of the particle at time is given by A ( cdot 3 t sqrt{alpha^{2}+beta^{2}} ) B . ( 3 t^{2} sqrt{alpha^{2}+beta^{2}} ) c. ( 3 t sqrt{alpha^{2}+beta^{2}} ) D. ( sqrt{alpha^{2}+beta^{2}} ) | 11 |

421 | In the figure shown ( mathrm{S} ) is the source of white light kept at a distance ( x_{0} ) from the plane of the slits. The source moves with a constant speed u towards the slits on the line perpendicular to the plane of the slits and passing through the slit ( S_{1} ). Find the instantaneous velocity (magnitude and direction) of the central maxima at time t having range ( 0 leq t<>d ) | 11 |

422 | The parameters for a particle that describe a uniform circular motion and a uniform velocity motion in a straight line are given below. Which one of them will you use to distinguish their motions A. Speed of both the particles B. Distance traveled by both the particles C. Average velocity of both the particles D. None of these | 11 |

423 | 31. What displacement at an angle 60° to the x-axis has an x-component of 5 m? i and j are unit vectors in x and y directions, respectively. a. 5î b. 5i +5 bar c. 5i +531 d . All of the above atamant | 11 |

424 | The relative velocity of ( B ) as seen from ( A ) is ( mathbf{A} cdot-8 sqrt{2} hat{i}+6 sqrt{2} hat{j} ) B. ( 4 sqrt{2} hat{imath}+3 sqrt{3} hat{j} ) c. ( 3 sqrt{5 hat{imath}}+2 sqrt{3} hat{jmath} ) D. ( 3 sqrt{2 hat{i}}+4 sqrt{3} hat{j} ) | 11 |

425 | Why do the passengers fall forward when a fast moving bus stops suddenly? | 11 |

426 | 0.5 m AA30 30. 71. A ball is projected from a point A with some velocity at an angle 30° with the horizontal as shown in Fig. 5.204. Consider a target at point B. The ball will hit the Fig. 5.204 target if it is thrown with a velocity vo equal to a. 5 ms-1 c. 7 ms-1 d. None of these b. 6 ms-1 | 11 |

427 | 52. A golfer standing on level ground hits a ball with a velocity of u = 52 ms at an angle a above the horizontal. If tan a = 5/12, then the time for which the ball is at least 15 m above the ground will be (take g = 10 ms) a. Is b. 2s c. 35 d. 4s | 11 |

428 | If the angle between the vectors ( vec{A} ) and ( vec{B} ) is ( theta, ) then the value of the product ( (vec{B} times vec{A}) cdot vec{A} ) equals A. ( B A^{2} sin theta ) B. ( B A^{2} cos theta sin theta ) c. ( B A^{2} cos theta ) D. zero | 11 |

429 | ( P ) is a point moving with constant speed ( 10 m / s ) such that its velocity vector always maintains an angle ( 60^{circ} ) with line ( O P ) as shown in figure ( (O ) is a fixed point in space). The initial distance between ( O ) and ( P ) is ( 100 m ). After what time shall ( P ) reach ( O ) A . ( 10 s ) B. ( 15 s ) c. ( 20 s ) D. ( 20 sqrt{3} s ) | 11 |

430 | A projectile is fired with a speed ( u ) at an angle ( theta ) with horizontal. Its speed when its direction of motion makes an angle ( alpha^{prime} ) with the horizontal is A . u ( sec theta cos alpha ) B. u ( sec theta sin alpha ) ( c cdot u cos theta sec alpha ) D. u ( sin theta sec alpha ) | 11 |

431 | 15. A particle moves along positive branch of the curve y=-, where x== , X and y are measured in meters and t in seconds, then a. The velocity of particle at t = 1 s is î+-j b. The velocity of particle at t= 1 sis 1 / 1 + . c. The acceleration of particle at t = 2 s d. The acceleration of particle at t = 2 s is î+2î . Ti 11 ca: 11. | 11 |

432 | A carom board ( (4 f t times 4 f t text { square }) ) has the queen at the centre. The queen, hit by the striker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen (i) from the centre to the front edge ( (i i) ) from the front edge to the hole and (iiii) from the centre of the hole. A. ( (i) frac{2}{3} sqrt{10} f t(i i) frac{4}{3} sqrt{10} f t(i i i) 2 sqrt{2} f t ) в. (i) ( frac{4}{3} sqrt{10} f t(i i) frac{4}{3} sqrt{10} f t(i i i) 2 sqrt{2} f t ) ( c ) (i) ( frac{4}{3} sqrt{10} f t(i i) frac{2}{3} sqrt{10} f t(i i i) 2 sqrt{2} f t ) ( D ) ( (i) frac{2}{3} sqrt{10} f t(i i) frac{2}{3} sqrt{10} f t(i i i) 2 sqrt{2} f t ) | 11 |

433 | If ( vec{A}+vec{B} ) is a unit vector along ( x ) -axis and ( vec{A}=hat{i}-hat{j}+hat{k} ) then what is ( vec{B} ? ) ( mathbf{A} cdot hat{j}+hat{k} ) B. ( hat{j}-hat{k} ) ( mathbf{c} cdot hat{i}+hat{j}+hat{k} ) D. ( hat{i}+hat{j}-hat{k} ) | 11 |

434 | In Fig. 5.201, the time taken by the projectile to reach from A to B ist. Then the distance AB is equal to ance ARCh from se taken 1 609 ut A 30° a. b. V3ut Fig. 5.201 3 c. √ut d. 2ut | 11 |

435 | Two identical balls ( P ) and ( Q ) are projected with same speeds in vertical plane from same point ( boldsymbol{O} ) with making projection angles with horizontal ( 30^{circ} ) and ( 60^{circ}, ) respectively and they fall directly on plane ( A B ) at points ( P^{prime} ) and ( Q^{prime} ) respectively. Which of the following statement is true about distance as given in options? A ( cdot A P^{prime}>A Q^{prime} ) B. ( A P^{prime}<A Q^{prime} ) c. ( A P^{prime} leq A Q^{prime} ) D. As there are complimentary projection angles | 11 |

436 | Q Type your question illustrated in Fig. Ball ( X ) has an initial velocity of ( 3.0 m s^{-1} ) in a direction along line ( A B ) Ball ( Y ) has a mass of ( 2.5 k g ) and an initial velocity of ( 9.6 m s^{-1} ) in a direction at an angle of ( 60^{circ} ) to line ( A B ) The two balls collide at point ( B ). The balls stick together and then trave along the horizontal surface in a direction at right-angles to the line ( boldsymbol{A B} ) as shown in Fig. Calculate the common speed ( V ) of the | 11 |

437 | 7. The resultant of P and Ở is perpendicular to P. What is the angle between P and 2 ? (a) cos-1 (PIQ) (b) cos-l(-PIQ) (c) sin-‘ (PIQ) (d) sin-‘(-PIQ) | 11 |

438 | 46. Two identical balls are set into motion simultaneously from equal heights h. While the ball A is thrown horizontally with velocity v, the ball B is just Ground released to fall by itself. Choose the alternative that best represents the motion of A and B with respect to an observer who moves with velocity v/2 with respect to the ground as shown in Fig A.24. А В A B 2. f | 11 |

439 | To how much angel does the earth revolve around sun in 2 days? | 11 |

440 | 18. A particle travels with speed 50 m s from the point (3, -7) in a direction Tử – 24j. Find its position vector after 3 s. | 11 |

441 | The physical quantity corresponding to the rate of change of displacement is A. speed B. velocity c. acceleration D. retardation | 11 |

442 | A balloon initially at rest, starts rising from the ground with an acceleration of ( 2 m / s^{2} . ) After ( 4 s, ) a stone is dropped from a balloon. In one second of time after the drop, the stone will cover a distance of ( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) ) A. ( 3.0 mathrm{m} ) в. 3.4 m ( mathbf{c} .3 .8 mathrm{m} ) D. ( 2.6 mathrm{m} ) | 11 |

443 | 10. A bullet is fired from horizontal ground at some angle passes through the point, where ‘R’ is the range of the bullet. Assume point of the fire to be origin and the bullet moves in x-y plane with x-axis horizontal and y-axis vertically upwards. Then angle of projection is (a) 30° (b) 37° (c) 53° (d) none +00 | 11 |

444 | 0 (0) 3 (0) 2 ed at an angle of 60° from the ground level 9. A stone projected at an angle of 60° from the 8 strikes at an angle of 30° on the roof of a building of height ‘h’. Then the speed of projection of the stone is. 30°C 260° (a) v2gh (b) Vogh (d) Vgh (c) /3gh | 11 |

445 | Two billiard balls are rolling on a flat table. One has velocity components ( boldsymbol{V}_{boldsymbol{x}}=mathbf{1} boldsymbol{m} / boldsymbol{s}, boldsymbol{V}_{boldsymbol{y}}=sqrt{mathbf{3}} boldsymbol{m} / boldsymbol{s} ) and the other has component ( V_{x}=2 m / s ) and ( V_{y}=2 m / s . ) If both the balls start moving from the same point the angle between their path is: A ( .60^{circ} ) B . 45 ( c cdot 22.5 ) D. ( 15^{circ} ) | 11 |

446 | The resultant of two forces ( P ) and ( q ) is right angle to ( P ), the resultant of ( P ) and ( Q ) acting at the same angle is at right angle to ( Q ). Prove that ( P ) is the geometric mean of ( Q ) and ( Q ) (i.e. ( P= ) ( sqrt{boldsymbol{Q} boldsymbol{q}} ? ) | 11 |

447 | A fly wheel rotating at 600 rev/min is brought under uniform deceleration and stopped after 2 minutes, then what is angular deceleration in ( r a d / s e c^{2} ? ) A ( cdot frac{pi}{6} ) в. ( 10 pi ) ( c cdot frac{1}{12} ) D. 300 | 11 |

448 | 14. A buoy is attached to three tugboats by three ropes. The tugboats are engaged in a tug-of-war. One tugboat pulls west on the buoy with a force Ē, of magnitude 1000 N. The second tugboat pulls south on the buoy with a force F of magnitude 2000 N. The third tugboat pulls northeast (that is, half way between north and east), with a force Fz of magnitude 2000 N. a. Express each force in unit vector form (î, j). b. Calculate the magnitude of the resultant force. | 11 |

449 | 28. Find the equation of trajectory of the boat. 1/3 C1=1=-(3)” c. x=l=u d. None of these d. None of these | 11 |

450 | Statement 1: If dot product and cross product of ( vec{A} ) and ( vec{B} ) are zero, it implies that one of the vector ( vec{A} ) and ( vec{B} ) must be a null vector. Statement 2: Null vector is a vector with | 11 |

451 | 7. Hailstones falling vertically with a speed of 10 mshi the wind screen (wind screen makes an angle 30° with the horizontal) of a moving car and rebound elastically. Find the velocity of the car if the driver finds the hailstone rebound vertically after striking. 30° Fig. 5.187 | 11 |

452 | A man walks ( 8 mathrm{m} ) towards East and then ( 6 mathrm{m} ) towards North. His magnitude of displacement is equal to: A . ( 10 mathrm{m} ) B. 14 ( m ) ( c cdot 2 m ) D. zero | 11 |

453 | A boy sitting on the top most berth in the compartment of a train which is just going to stop on a railway station, drops an apple aiming at the open hand of his brother situated vertically below his hands at a distance of about ( 2 mathrm{m} ) The apple will fall A. In the hand of his brother B. Slightly away from the hands of his brother in the direction of motion of the train c. Slightly away from the hands of his brother in the direction opposite to the direction of motion of the train D. None of these | 11 |

454 | What is a projectile? Give example. | 11 |

455 | A wheel has moment of inertia ( 10^{-2} k g-m^{2} ) and is making 10 rps. The torque required to stop it in 5 secs is A. 12.56 B. 9.42 ( c cdot 6.28 ) D. 3.14 | 11 |

456 | A man is walking on a road with a velocity ( 3 k m / h . ) Suddenly rain starts falling. Velocity of rain is ( 10 mathrm{km} / mathrm{h} ) in vertically downward direction. The relative velocity of the rain with respect to man is A ( cdot sqrt{13} k m / h r ) B. ( sqrt{7} mathrm{km} / mathrm{hr} ) c. ( sqrt{109} mathrm{km} / mathrm{hr} ) D. ( 13 mathrm{km} / mathrm{hr} ) | 11 |

457 | Speed of the current. | 11 |

458 | A car travels along a circular path of radius ( left(frac{50}{pi}right) mathrm{m} ) with a speed of ( 10 mathrm{m} / mathrm{s} ) Then what is its displacement after 17.5 seconds. ( A cdot frac{50 sqrt{2}}{pi} ) B. ( frac{50 sqrt{3}}{pi} ) c. ( frac{100 sqrt{2}}{pi} ) D. 175 | 11 |

459 | 1/2 MIIS luwalus 101 d. 2. A river is flowing from west to east at a speed of 5 m per min. A man on the south bank of the river, capable of swimming at 10 m per min in still water, wants to swim across the river in the shortest time. He should swim in a direction (IIT JEE, 1983) a. Due north b. 30° east of north c. 30° west of north d. 60° east of north worth | 11 |

460 | The position of a particle as a function of time is described by relation ( boldsymbol{x}= ) ( 3 t-3 t^{2}+t^{3} ) where the quantities are expressed in S.I. units. If mass of the particle be ( 10 mathrm{kg} ), the work done in first three seconds is A . 10 B. 30 J c. ( 300 J ) D. 675 J | 11 |

461 | A train ( 100 mathrm{m} ) long travelling at ( 40 mathrm{m} / mathrm{s} ) starts overtaking another train ( 200 mathrm{m} ) long travelling at ( 30 mathrm{m} / mathrm{s} ). The time taken by the first train to pass the second train completely is: A. 30 B. 40 ( c .50 mathrm{s} ) D. 60 s | 11 |

462 | A helicopter is to reach a point ( 200000 m ) east of his existing place. Its velocity relative to wind blowing at ( 30 k m h^{-1} ) from northwest taking scheduled arrival time duration as 40minute is B. ( 279 hat{i}+21 hat{j} ) c. ( 729 hat{i}+12 hat{j} ) D. ( 12 hat{i}+729 hat{j} ) | 11 |

463 | Prove that the vectors ( 2 hat{i}-3 hat{j}-hat{k} ) and ( -6 hat{i}+9 hat{j}+3 hat{k} ) are parallel. | 11 |

464 | 9. A particle is projected from a stationary Fig. A.46 trolley. After projection, the trolley moves with a velocity 2/15 m/s. For an observer on the trolley, the direction of the particle is as shown in the figure while for the observer on the ground, the ball rises vertically. The maximum height reached by the ball from the trolley is h meter. The value of h will be (W.r.t. Trolley) 60 0 10 m/s Fig. A.47 | 11 |

465 | The position vector of a particle is ( vec{r}= ) ( (a cos omega t) hat{i}+(a sin omega t) hat{j} . ) The velocity of the particle is A. Parallel to position vector B. Perpendicular to position vector c. Directed towards the origin D. Directed from away from the origin | 11 |

466 | Velocity of particle moving along a straight line at any time ( t ) is given by ( v=cos left(frac{pi}{3} tright) . ) The distance travelled by the particle in the first two seconds is equal to A ( cdot frac{sqrt{3}}{2 pi} ) B. ( frac{3 sqrt{3}}{2 pi} ) ( c cdot frac{3 sqrt{3}}{pi} ) D. zero | 11 |

467 | What is a projectile? Derive an equation of the path of a projectile | 11 |

468 | 39. An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 rpm, find the acceleration of a point on the tip of a blade. | 11 |

469 | SIP- Illustration 5.25 A particle is projected with relocity angle with horizontal. Calculate the time when it is movin perpendicular to initial direction. Also calculate the velo at this position. Initial direction Fig. 5.42 | 11 |

470 | If a body placed at the origin is acted upon by a force ( overline{boldsymbol{F}}=(hat{boldsymbol{i}}+hat{boldsymbol{j}}+sqrt{mathbf{2}} hat{boldsymbol{k}}) ) then which of the following statements are correct? 1.Magnitude of ( overline{boldsymbol{F}} ) is ( (2+boldsymbol{s} boldsymbol{q} boldsymbol{r} boldsymbol{t} boldsymbol{2}) ) 2.Magnitude of ( overline{boldsymbol{F}} ) is 2 3. ( bar{F} ) makes an angle of ( 45^{0} ) with the ( Z ) – axis. 4. ( bar{F} ) makes an angle of ( 30^{0} ) with the ( Z ) axis. Select the correct answer using the codes given below. A . 1 and 3 B. 2 and 3 c. 1 and 4 D. 2 and 4 | 11 |

471 | A ball is projected on smooth inclined plane in direction perpendicular to line of greatest slope with velocity of ( 8 boldsymbol{m} / boldsymbol{s} ) t’s speed after ( left.1 s text { is (take } g=10 mathrm{m} / mathrm{s}^{2}right) ) ( A cdot 10 mathrm{m} / mathrm{s} ) B. ( 15 mathrm{m} / mathrm{s} ) ( c cdot 12 m / s ) ( D cdot 16 mathrm{m} / mathrm{s} ) | 11 |

472 | Find the time taken by the boat to reach the opposite bank. | 11 |

473 | Vectors ( bar{A} ) and ( bar{B} ) are equal in magnitude. The magnitude of ( bar{A}+bar{B} ) is larger than the magnitude of ( overline{boldsymbol{A}}-overline{boldsymbol{B}} ) by a factor of ( n, ) then the angle between them is A ( cdot 2 tan ^{-1}(1 / n) ) B. ( tan ^{-1}(1 / n) ) c. ( tan ^{-1}(1 / 2 n) ) D. ( 2 tan ^{-1}(1 / 2 n) ) | 11 |

474 | In vertical circle, can the motion be uniform circular motion? A. yes B. no c. sometimes D. none of these | 11 |

475 | The captain of a plane wishes to proceed due west. The cruising speed of the plane is ( 245 m / s ) relative to the air. A weather report indicates that a ( 38 m / s ) wind is blowing from the south to the north. In what direction, measured to due west, should the pilot head the plane relative to the air? (in degrees) ( A cdot 8 ) B. 9 ( c .6 ) D. 5 | 11 |

476 | Tlustration 5.44 A man wishes to cross a river in a boat. If crosses the river in minimum time he takes 10 min with drift of 120 m. If he crosses the river taking shortest route. he takes 12.5 min. Find the velocity of the boat with respect to water. | 11 |

477 | 43. The velocity of point A on the rod is 2 ms(leftwards) at the instant shown in Fig. 6.326. The velocity of the point B on the rod at this instant is 60° VA = 2 ms-‘ Fig. 6.326 2 mst b. 1 ms-1 ms-1 d. 13 mst 2 ms | 11 |

478 | 2. The resultant of A + B is Ã On reversing the vector B the resultant becomes . What is the value of R + RŽ ? (a) A2 + B2 (b) A2 – B2 (c) 2(A2 + B2) (d) 2(A2 – B2) | 11 |

479 | A body of mass Mkg is on the top point of a smooth hemisphere of radius ( 5 mathrm{m} ). It is released to slide down the surface of hemisphere it leaves the surface when its velocity is ( 5 m s^{-1} ) At this instant the angle made by the radius vector of the body with the vertical is ( left(g=10 m s^{-2}right) ) A ( cdot cos ^{-1}left(frac{3}{4}right) ) B . ( 45^{circ} ) ( c cdot 60 ) D. ( 90^{circ} ) | 11 |

480 | 13. A vector a is turned without a change in its length through a small angle do. The value of|Aal and Aa are respectively (a) 0, a de (b) a do, o (c) 0,0 (d) None of these | 11 |

481 | Find the unit vector in the direction of ( mathbf{3} hat{mathbf{i}}-mathbf{6} hat{mathbf{j}}+mathbf{2} widehat{mathbf{k}} ) | 11 |

482 | In uniform circular motion A. both velocity and speed are constant B. speed is constant but velocity changes C. both speed and velocity change D. velocity is constant but speed changes | 11 |

483 | A solid body rotates about a stationary axis according to the law ( varphi=a t-b t^{3}, ) where ( a=6.0 mathrm{rad} / mathrm{s} ) and ( boldsymbol{b}=mathbf{2} . mathbf{0} boldsymbol{r} boldsymbol{a} boldsymbol{d} / boldsymbol{s}^{mathbf{3}} ) Find the mean values of the angular velocity and angular acceleration averaged over the time interval between ( t=0 ) and the complete stop. The sum of their magnitudes is x. Find the value of ( mathbf{x} ) | 11 |

484 | A body is projected horizontally from the top of a hill with a velocity of ( 9.8 m / s ) What time elapses before the vertical velocity is twice the horizontal velocity? A . 0.5 sec B. 1 sec ( c .2 s e c ) D. 1.5 sec | 11 |

485 | Rain is falling vertically. A man running on the the road keeps his umbrella tilted but a man standing on the street keeps his umbrella vertical to protect himself from the rain. But both of them keep their umbrella vertical to avid the vertical sun-rays. Explain. | 11 |

486 | A fielder on the ground throws a ball at an angle of ( 15^{circ} ) to the horizontal with velocity ( V_{A} ) at the wicket to dismiss the batsman. Had he thrown the ball at ( 45^{circ} ) with a speed ( V_{B} ) to hit the wicket, then ( frac{V_{B}}{V_{A}} ) is ( ^{A} cdot frac{1}{sqrt{3}} ) в. ( sqrt{2} ) c. ( sqrt{3} ) D. ( frac{1}{sqrt{2}} ) | 11 |

487 | A projectile ofmass ( m ) is thrown with a velocity v making an angle ( 60^{circ} ) with the horizontal, neglecting air resistance, the change in momentum from the departure A to its arrival at B, along the vertical directions: ( A cdot 2 m ) B. ( sqrt{3} mathrm{mv} ) ( c .3 m v ) D. ( frac{m v}{sqrt{3}} ) | 11 |

488 | A thin uniform bar of length L and mass ( 8 mathrm{m} ) lies on a smooth horizontal table. Two point masses ( m ) and 2 m are moving in the same horizontal plane from opposite sides of the bar with speeds ( 2 v ) and ( v ) respectively. The masses stick to the: A ( cdot frac{6 v}{5 l} ) в. ( frac{3 v}{5 l} ) c. ( frac{6 v}{11 l} ) D. ( frac{6 v}{l} ) | 11 |

489 | If the body is moving in a circle of radius ( r ) with a constant speed ( V ), its angular velocity is A ( cdot V^{2} / r ) в. ( V r ) c. ( V / r ) D. ( r / V ) | 11 |

490 | The angular velocity of rotation of hour hand of a watch is how many times the angular velocity of Earth’s rotation about its own axis? A. Three B. Four c. Two D. six | 11 |

491 | 43. A car is moving in east direction. It takes a right turn an moves along south direction without change in its spee What is the direction of average acceleration of the car a. North east b. South east c. North west d. South west 11 | 11 |

492 | 3 m 3. Spotlight S rotates in a horizontal plane with constant angular velocity of 0.1 rad s . The spot of light P moves along the wall at a distance of 3 m. The PO velocity of the spot P when @ = 45° spot P when 0 = 45 Fig. A.50 is ms? (IIT JEE, 1987) | 11 |

493 | What will be the effect on the centripetal acceleration, if both the speed and the radius of the circular path of the body are doubled? | 11 |

494 | 23. A particle has initial velocity 4i + 4 ms and an acceleration -0.4i ms?, at what time will its speed be 5 ms? a. 2.5 S b . 17.5 S c. S d. 8.5 s | 11 |

495 | 25. Two particles are thrown horizontally in opposite directions with velocities u and 2u from the top of a high tower. The time after which their radius of curvature will be mutually perpendicular is a. 24 b. 2 c. – 1 u al u 12 g 2 g | 11 |

496 | The locus of a projectile relative to another projectile is a A. straight line B. circle c. ellipse D. parabola | 11 |

497 | The position of a particle is given by ( vec{r} ) ( =3 t hat{i}+2 t^{2} hat{j}+5 hat{k}, ) where ( t ) is in seconds and the coefficients have the proper units for ( r ) to be in metres. The direction of velocity of the particle at ( t=1 ) s is: ( A cdot 53^{circ} ) with ( x ) -axis B. 37 ( ^{circ} ) with ( x ) -axis c. ( 30^{circ} ) with ( y ) -axis D. ( 60^{circ} ) with ( y ) -axis | 11 |

498 | A particle projected from the origin ( (x=y=0) ) moves in ( x y ) plane so that its velocity is ( v=(2 hat{i}+4 x hat{j}) mathrm{m} / mathrm{s}, ) when it is at point ( (x, y) ) m. ( (hat{i} text { and } hat{j} ) are the unit vectors along ( x ) and ( y ) axis). What is the value of ( y, ) when ( x=3 ) A . 15 B. 10 ( c .9 ) D. 8 | 11 |

499 | A projectile is fired with an initial speed of ( 500 quad m s^{-1} ) horizontally from the top of a cliff of height ( 19.6 mathrm{m} ). At what distance from the foot of the cliff does it strike the ground? | 11 |

500 | A particle is projected from ground with some initial velocity making an angle ( 45^{circ} ) with the horizontal. It reaches at height of ( 7.5 mathrm{m} ) above the ground while it travels a horizontal distance of ( 10 mathrm{cm} ) from the point of projection. The initia speed of the projection is ( A cdot 5 m / s ) B. ( 10 mathrm{m} / mathrm{s} ) ( c cdot 20 m / s ) D. ( 40 mathrm{m} / mathrm{s} ) | 11 |

501 | The velocity of the body at the end of 1 s from the start is: A . 2N в. ( frac{M+2 N}{4} ) c. ( 2(M+N) ) D. ( frac{2 M+N}{4} ) | 11 |

502 | On rotating a wheel of radius ( 4 m, a ) force of ( 20 N ) is applied at an angle ( 30^{circ} ) to the radius, at a point of application. The resulting torque on the wheel is: ( mathbf{A} cdot 80 N-m ) B. ( 60 N-m ) c. ( 40 N-m ) D. ( 20 N-m ) | 11 |

503 | A wheel starts from the rest and attains an angular velocity of 20 radian/s after being uniformly accelerated for 10 s.The total angle in radian through which it has turned in 10 second is A ( .20 pi ) в. ( 40 pi ) ( c .100 ) D. ( 100 pi ) | 11 |

504 | istration 5.54 A person standing on a road has to hold umbrella at 60° with the vertical to keep the rain away. We throws the umbrella and starts running at 20 ms. He find that rain drops are hitting his head vertically. Find the speed of the rain drops with respect to (a) the road and (b) the moving person. 1600 lvl = 0 Fig. 5.106 Fig. 5.107 | 11 |

505 | Give an example of the motion of a body moving with a constant speed, but with a variable velocity. Draw a diagram to represent such a motion. | 11 |

506 | A rock is launched upward at 45°. A bee moves along the trajectory of the rock at a constant speed equal to the initial speed of the rock. What is the magnitude of acceleration (in ms) of the bee at the top point of the trajectory? For the rock, neglect the air resistance. | 11 |

507 | 15. The direction of a projectile at a certain instant is inclined at an angle a to the horizontal; after t second, it is inclined at an angle B. Prove that the horizontal component of the gt velocity of the projectile is – tan a – tan ß | 11 |

508 | When a body moves with a constant speed along a circle: A. no work is done on it B. no acceleration is produced in the body C. no force acts on the body D. its velocity remains constant | 11 |

509 | Two forces each of ( 10 N ) act at an angle ( 60^{circ} ) with each other. The magnitude ( & ) direction of the resultant with respect to one of the vectors is | 11 |

510 | A mass is performing vertical circular motion(see figure).lf The average velocity of theparticle is increased, then at which point thestring will break: ( A cdot A ) B. B ( c cdot c ) D. | 11 |

511 | A body of mass ( 5 k g ) is acted upon by two perpendicular force ( 8 N ) and ( 6 N ) find the magnitude and direction the acceleration: A ( cdot 3 m s^{-2}, theta=cos ^{-1}(0.8) ) from ( 8 N ) B . ( 2 m s^{-2}, theta=cos ^{-1}(0.6) ) from ( 6 N ) c. ( 3 m s^{-2}, theta=cos ^{-1}(0.9) ) from ( 6 N ) D. ( 5 m s^{-2}, theta=cos ^{-1}(0.81) ) from ( 8 N ) | 11 |

512 | Illustration 5.52 A man moving with 5 ms observes rain falling vertically at the rate of 10 ms. Find the speed and direction of the rain with respect to ground. | 11 |

513 | There are three particles shown in the figure as I, II and III. The velocity and acceleration vectors associated with the motion of three particles are shown. Which of the above could represent the velocity and acceleration vectors for a projectile following a parabolic path? I. II. III. A. I only B. II only c. III only D. I and II only E. II and III only | 11 |

514 | A body is projected vertically upwards with a velocity of ( 19.6 ~ m / s . ) The total time for which the body will remain in the air is (Take ( boldsymbol{g}=mathbf{9 . 8 m} / boldsymbol{s}^{2} ) A . ( 4 s ) B. ( 6 s ) ( mathrm{c} .9 mathrm{s} ) D. 12 s | 11 |

515 | A train of length 200 m travelling at 30 ( m s^{-1} ) overtakes another train of length ( 300 mathrm{m} ) travelling at ( 20 mathrm{ms}^{-1} ). The time taken by the first train to pass the second is A . 30 sec B. 40 sec c. ( 50 mathrm{sec} ) D. 60 sec | 11 |

516 | 27. Obtain the total time taken to cross the river. a. (3d/5)1/3 c. (60/5)12 b. (60/5)1/3 d. (2d/3)1/3 11 | 11 |

517 | A person climbs up a stopped escalator in ( 60 s . ) If standing on the same escalator but escalator running with constant velocity, he takes 40 s. How much time is taken by the person to walk up in the moving escalator? A. ( 37 s ) в. 27 s ( c cdot 24 s ) D. ( 45 s ) | 11 |

518 | A man can swim in still water with a velocity 5 m/s. He wants to reach at directly opposite point on the other bank of a river which is flowing at a rate of ( 4 m / s . ) River is 15 m wide and the man can run with twice the velocity as compared with velocity of swimmer with respect to river. If he swims perpendicular to river flow and then run along the bank. Time, in seconds, taken by him to reach the opposite point is A. 4.0 B. 4.2 ( c .5 .4 ) D. 3.6 | 11 |

519 | 40. A ball thrown by one player reaches the other in 2 s. The maximum height attained by the ball above the point of projection will be about a. 2.5 m b. 5 m c. 7.5 m d. 10 m | 11 |

520 | 12. An object is projected from origin in x-y plane in which velocity changes according to relation v=ai + bxſ. Path of particle is a. Hyperbolic b . Circular c. Elliptical d. Parabolic le 200 | 11 |

521 | Illustration 5.66 Find the time period of the meeting of minute hand and second hand of a clock. | 11 |

522 | A stone is projected with a initial velocity at an angle to the horizontal. small piece separates from the stone before the stone reaches its maximum height. Then this piece will A. fall to the ground vertically B. fly side by side with the parent stone along parabolic path c. fly horizontally initially and will trace a different parabolic path D. lag behind the parent stone, increasing the distance from it. | 11 |

523 | 4. Four bodies P, Q, R and Sare projected with equal velocities having angles of projection 15°, 30°, 45° and 60° with the horizontal respectively. The body having shortest range is (a) P (b) e (c) R (d) s | 11 |

524 | A vector ( overline{boldsymbol{m}} ) of magnitude ( 2 sqrt{101} ) in the direction of internal bisector of the angle between the vector ( bar{b}=8 hat{i}-6 hat{j}- ) ( 6 hat{k} ) and ( bar{c}=4 hat{i}-3 hat{j}+4 hat{k} ) is ( A ) B . ( 16 hat{i}-12 hat{j}+2 hat{k} ) ( frac{-16 hat{i}+12 hat{j}+2 hat{k}}{5} ) D . ( 16 hat{i}+12 hat{j}+2 hat{k} ) | 11 |

525 | 34. Projection angle with the horizontal is: | 11 |

526 | A particle of mass ( 1 mathrm{kg} ) has a velocity of ( 2 mathrm{m} / mathrm{s} . ) A constant force of ( 2 mathrm{N} ) acts on the particle for 1 s in a direction perpendicular to its initial velocity. Find the velocity and displacement of the particle at the end of 1 s. | 11 |

527 | An object may have This question has multiple correct options A. Varying speed without having varying velocity B. Varying velocity without having varying speed C. Non zero acceleration without having varying velocity D. Non zero acceleration without having varying speed | 11 |

528 | There are three forces acting on an object : 6 N to the left, 5 N to the right and ( 3 mathrm{N} ) to the left.What is the net force acting on the object? ( A cdot 4 N ) B. 4 N left c. 4 N right D. 8 N left E. None of above | 11 |

529 | Two particles having masses ( 1 k g ) and 7 kg respectively attract each other. Initially they are at rest and infinite separation.The velocity of approach of the particles are at a separation of ( 1 boldsymbol{m} ) is (G=universal gravitational constant) ( begin{array}{lll}text { A } cdot sqrt{2} G & text { m/s }end{array} ) B . ( 4 sqrt{G} ) m/s c. ( sqrt{frac{G}{2} m / s} ) D. ( frac{G}{4} m / s ) | 11 |

530 | 65. The horiz The horizontal range and maximum height attained by a roiectile are R and H, respectively. If a constant horizontal acceleration a = g/4 is imparted to the projectile due to wind, then its horizontal range and maximum height will be TH a. (R+H), b. R+- 1,2H 2 c. (R+ 2H), H d. (R+ H), H | 11 |

531 | The objects pictured above are coins moving around on a record player. The coins are not sliding on the record player surface. Which coins is moving faster and how many times faster it is moving than the other one? The space between each vertical line along the horizontal arrow is one- seventh the radius of the circular record player surface. A. 1-three times faster than slowest B. 3-five-seventh’s faster than slowest c. 3-five times faster than slowest D. 1-five-seventh’s faster than slowest E. 2 -three-seventh’s faster than slowest | 11 |

532 | A wall clock has a ( 5 mathrm{cm} ) long minute hand. The average velocity of the tip of the hand reaching 06.00 hrs. to 18.30 hrs. is A ( .2 .2 times 10^{-4} mathrm{cm} / mathrm{s} ) B. ( 1.2 times 10^{-4} mathrm{cm} / mathrm{s} ) C . ( 5.6 times 10^{-4} mathrm{cm} / mathrm{s} ) D. ( 3.2 times 10^{-4} mathrm{cm} / mathrm{s} ) | 11 |

533 | A motor ship covers the distance of ( 300 k m ) between two localities on a river in 10 hours downstream and in 12 hours upstream. Find the flow velocity of the river assuming that these velocities are constant. A. ( 2.0 mathrm{km} / mathrm{h} ) B. 2.5 km/h ( c .3 mathrm{km} / mathrm{h} ) D. 3.5 km/h | 11 |

534 | 8. A boat is moving with a velocity 3î +4j with respect to ground. The water in the river is moving with a velocity -3i – 4ſ with respect to ground. The relative velocity of the boat with respect to water is a. 8 ] b. 6i -87 c. 6i +8î d. 5/2 | 11 |

535 | In the case of uniform circular motion, which one of the following physical quantities does not remain constant? A . mass B. speedd c. linear momentum D. kinetic energy | 11 |

536 | Fill in the blank. When body is performing uniform circular motion, its ( _{-}-_{-}-_{-}- ) changes at every points. | 11 |

537 | Show that there are two values of time for which a projectile is at the same height. Also show mathematically that the sum of these two times is equal to the time of flight. | 11 |

538 | A train of length ( 100 m ) travelling at ( 20 m / s ) overtakes another of length ( 200 m ) travelling at ( 10 m / s . ) The time taken by the first train to pass the second train is A . ( 30 s ) в. ( 50 s ) ( c cdot 10 s ) D. ( 40 s ) | 11 |

539 | If ( R ) is the maximum horizontal range of a particle, then the greatest height attained by it is: A. ( R ) в. ( 2 R ) c. ( frac{R}{2} ) D. ( frac{R}{4} ) | 11 |

540 | A wheel having a diameter of 3 m starts from rest and accelerates uniformly to an angular velocity of 210 r.p.m.in 5 seconds. Angular acceleration of the wheel is A ( cdot 4.4 pi frac{r a d}{s^{2}} ) В. ( _{3.3 pi} frac{r a d}{s^{2}} ) c. ( _{2.2 pi} frac{r a d}{s^{2}} ) D. ( _{1.1 pi} frac{r a d}{s^{2}} ) | 11 |

541 | A body is projected up such that its position vector with time as ( vec{r}= ) ( left{3 t hat{i}+left(4 t-5 t^{2}right) hat{j}right} m . ) Here, tis in seconds. Find the time and ( x- ) coordinate of particle when its ( y- ) coordinate is zero. | 11 |

542 | Two projectiles are thrown at angles ( Theta ) and ( left(90^{circ} Thetaright) ) with same speed. The ratio of their horizontal ranges are ( A cdot 1: 1 ) B. ( 1: tan theta ) ( c cdot tan theta: 1 ) ( mathbf{D} cdot tan ^{2} Theta: 1 ) | 11 |

543 | Which cannonball reaches a higher elevation? ( A cdot A ) B. B c. Both reaches same height D. Cannot be judged | 11 |

544 | If ( S ) identical rain drops each falling with terminal velocity v combine to form a big drop during their fall the terminal velocity of big drop formed is : ( A ) B. ( frac{v}{8} ) ( c cdot 4 v ) D. 2v | 11 |

545 | the car is moving towards east with a speed of ( 25 mathrm{km} / mathrm{h} ). To the driver of the car, a bus appears to move towards north with a speed of ( 25 sqrt{3} k m / h . ) What is the actual velocity of the bus? A ( cdot 50 k m / h, 30^{circ} ) east of north B. ( 50 k m / h, 30^{circ} ) north of east ( mathrm{c} cdot 25 k m / h, 30^{circ} ) east of north D. ( 25 k m / h, 30^{circ} ) north of east | 11 |

546 | The diagram below shows four orange spheres moving in circular paths at constant speeds. The speeds are indicated by the red arrows. The radius of the circular path for each indicated by the green arrows. The mass of each sphere is labeled inside the boundary of the sphere How do the sphere rank, according to the magnitudes of their accelerations, | 11 |

547 | If two forces of equal magnitudes act simultaneously on a body in the east and the north directions then A. The body will displace in the north direction B. The body will displace in the east direction c. The body will displace in the north-east direction D. The body will remain at the rest | 11 |

548 | Illustration 3.11 A particle is moving with velocity v = 100 m s. If one of the rectangular components of a velocity is 50 ms. Find the other component of velocity and its angle with the given component of velocity. | 11 |

549 | The position vector of a particle is ( r= ) ( (a cos omega t) hat{i}+(a sin omega t) hat{j} . ) The velocity vector of the particle is A. parallel to position vector B. perpendicular to position vector c. directed towards the origin D. directed away from the origin | 11 |

550 | If a particle moves in a circle with constant speed, its velocity : A. remains constant B. changes in magnitude c. changes direction D. changes both in magnitude and directions | 11 |

551 | — Coro One Illustration 5.10 Two graphs of the same projectile motion in the x- y-plane) projected from origin are shown in Fig. 5.10. X-axis is along horizontal direction and Y-axis is vertically upwards. Take g = 10 m s. (²20) (2,0) -t(s) (m) (a) (6) | 11 |

552 | What are the speeds of two objects if they move uniformly towards each other, they get ( 4 mathrm{m} ) closer in each second and if they move uniformly in the same direction with the original speeds they get ( 4 mathrm{m} ) closer in each ( 10 mathrm{sec} ? ) A. ( 2.8 mathrm{m} / mathrm{s} ) and ( 1.2 mathrm{m} / mathrm{s} ) B. 5.2 ( mathrm{m} / mathrm{s} ) and ( 4.6 mathrm{m} / mathrm{s} ) c. ( 3.2 mathrm{m} / mathrm{s} ) and ( 2.1 mathrm{m} / mathrm{s} ) D. 2.2 ( mathrm{m} / mathrm{s} ) and ( 1.8 mathrm{m} / mathrm{s} ) | 11 |

553 | A car with a vertical windsheld moves in a rain storm at a speed of ( 40 mathrm{km} / mathrm{hr} ) The rain drops fall vertically with constant speed of ( 20 m / s . ) The angle at which rain drops strike the windsheild is A. ( tan ^{-1} frac{5}{9} ) в. ( tan ^{-1} frac{9}{5} ) c. ( quad ) tan ( ^{-1} frac{3}{2} ) D. ( tan ^{-1} frac{2}{3} ) | 11 |

554 | It is possible to project a particle with a given speed in two possible ways so that it has the same horizontal range ( boldsymbol{R} ) The product of the times taken by it in the two possible ways is A ( cdot frac{R}{g} ) в. ( frac{2 R}{g} ) c. ( frac{3 R}{g} ) D. ( frac{4 R}{g} ) | 11 |

555 | The velocity at the maximum height of projectile is half of its initial velocity projection. The angle of projection is A . ( 30^{circ} ) B . ( 45^{circ} ) ( c cdot 60^{circ} ) D. ( 76^{circ} ) | 11 |

556 | 2. The coordinates of a particle moving in a plane are give by X(t) = a cos(pt) and y(t) = b sin(pt), where a, bls and p are positive constants of appropriate dimension Then (IIT JEE, 1999 a. The path of the particle is an ellipse. b. The velocity and acceleration of the particle are normal to each other at t = Td2p. c. The acceleration of the particle is always directed towards a focus. d. The distance travelled by the particle in time interval t=0 to t = 7/2p is a. | 11 |

557 | W 5vou que veuww 38. A cyclist is riding with a speed of 27 kmh. As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.5 ms?. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn? | 11 |

558 | A bicycle travels ( 3.2 k m ) due east in ( 0.1 h ) the ( 3.2 k m ) at 15.0 degrees east of north in ( 0.21 h ), and finally another ( 3.2 k m ) due east in ( 0.1 h ) to reach its destination. The time lost in turning is negligible. What is the average velocity for the entire trip? (in ( mathrm{km} / mathrm{h}) ) A . 20 B . 21 c. 19 D. 30 | 11 |

559 | A cyclist bends while taking turn to A. Reduce friction B. Generate required centripetal force c. Reduce apparent weight D. Reduce speed | 11 |

560 | 30. As shown in Fig. 6.315, if acceleration of M with respect to ground is 2 ms, then sin 37° = 3/5 cos 37° = 4/5 a = 2 ms-2 M 37°N Fig. 6.315 a. Acceleration of m with respect to M is 5 ms. b. Acceleration of m with respect to ground is 5 ms2 c. Acceleration of m with respect M is 2 ms 2 d. Acceleration of m with respect to ground is 10 ms?. | 11 |

561 | In a Circus, a motor-cyclist having mass of ( 50 k g ) moves in a spherical cage of radius ( 3 m . ) Calculate the least velocity with which he must pass the highest point without losing contact. Also calculate his angular speed at the highest point. | 11 |

562 | An engine of a train moving with uniform acceleration passes an electric pole with velocity u and the last compartment with velocity v. The middle part of the train passes past the same pole with a velocity of A ( cdot frac{u+v}{2} ) в. ( frac{u^{2}+v^{2}}{2} ) c. ( sqrt{frac{u^{2}+v^{2}}{2}} ) D. ( sqrt{frac{u^{2}-v^{2}}{2}} ) | 11 |

563 | A man wants to reach point B on the opposite bank of river flowing at a speed as shown in figure. What minimum speed relative to water should the man have so that he can reach point B? | 11 |

564 | A train ( S 1, ) moving with a uniform velocity of ( 108 mathrm{km} / mathrm{h} ), approaches another train ( S 2 ) standing on a platform. An observer 0 moves with a uniform velocity of ( 36 mathrm{km} / mathrm{h} ) towards ( S 2 ) as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When 0 is 600 m away from ( S 2 ) and distance between ( S 1 ) and ( S 2 ) is ( 800 m ) the number of beats heard by 0 is (Speed of the sound ( = ) ( 330 mathrm{m} / mathrm{s} ) | 11 |

565 | A helicopter flies horizontally with constant velocity in a direction ( boldsymbol{theta} ) east of north between two points ( boldsymbol{A} ) and ( boldsymbol{B}, ) at distance d apart. Wind is blowing from south with constant speed u; the speed of helicopter relative to air is nu, where ( mathbf{n}>1 . ) Find the speed of the helicopter along AB. The helicopter returns from B to A with same speed nu relative to air in same wind. Find the total time for the journeys. | 11 |

566 | A player throws a ball which reaches the other players in 4 sec.If the height of each player is ( 1.8 m . ) The maximum height attained by the ball above the ground is ( -ldots-ldots ) A . 19.4 B. 20.4 c. 21.4 D. 22.4 | 11 |

567 | 9. A car is moving towards east with a speed of 25 kmh. To the driver of the car, a bus appears to move towards north with a speed of 2513 km h-. What is the actual velocity of the bus? a. 50 km h, 30º E of N b. 50 km h, 30° N of E c. 25 km h, 30° E of N d. 25 km h, 30° N of E | 11 |

568 | A body of mass 5 kg is raised vertically to a height of ( 10 mathrm{m} ) by a force of ( 170 mathrm{N} ) the velocity of the body at this height will be ( mathbf{A} cdot 15 m / s ) в. ( 37 m / s ) c. ( 9.8 m / s ) D. ( 21.9 mathrm{m} / mathrm{s} ) | 11 |

569 | A body of mass ( mathrm{m} ) is projected from ground with speed ( u ) at an angle ( theta ) with horizontal the power delivered by gravity to it at half of maximum heigh from ground is | 11 |

570 | If the velocity of a particle is ( boldsymbol{v}=boldsymbol{A} boldsymbol{t}+ ) ( B t^{2}, ) where ( A ) and ( B ) are constants, then the distance travelled by it between 1 s and ( 2 s ) is A ( cdot frac{3}{2} A+4 B ) B. ( 3 A+7 B ) c. ( frac{3}{2} A+frac{7}{3} B ) D. ( frac{A}{2}+frac{B}{3} ) | 11 |

571 | 8. Two forces P and Q acting at a point are such that if P is reversed, the direction of the resultant is turned through 90°. Prove that the magnitudes of the forces are equal. | 11 |

572 | U. TOM 010 21. Raindrops are hitting the back of a man walking at a of 5 kmh. If he now starts running in the same direct with a constant acceleration, the magnitude of the velo of the rain with respect to him will a. gradually increase b. gradually decrease c. first decrease then increase d. first increase then decrease | 11 |

573 | In projectile motion, power of the gravitational force This question has multiple correct options A. is constant throughout B. is negative for first half, zero at topmost point and positive for rest half c. varies linearly with time D. is positive for complete path | 11 |

574 | 3. A body is projected vertically up with a velocity v and after some time it returns to the point from which it was projected. The average velocity and average speed of the body for the total time of flight are (a) 7/2 and v/2 (b) O and v/2 (c) 0 and 0 (d) v/2 and 0 | 11 |

575 | A ball is projected from the ground at an angled of ( 45^{circ} ) with the horizontal surface. It reaches a maximum height of ( 120 mathrm{m} ) and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of ( 30^{circ} ) with the horizontal surface. The maximum height it reaches after the bounce, in metres, is | 11 |

576 | If a disc starting from rest acquires an angular velocity of 240 revolution/ min in ( 10 s, ) then its angular acceleration will be A . 1.52 rads( ^{-1} ) B. 3.11 rads ( ^{-1} ) c. 2.51 rads ( ^{-1} ) D. 1.13 rads( ^{-1} ) | 11 |

577 | A gramophone turntable rotating at an angular velocity of 3 rad( / )s stops after one revolution. Find the angular retardation. (in ( left.r a d / s^{2}right) ) ( mathbf{A} cdot 0.698 ) B. 0.125 c. 0.569 D. 0.716 | 11 |

578 | Assertion In case of uniform linear motion, acceleration remains zero. Reason Velocity remains constant in uniform linear motion. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

579 | Matching con iven and in list 10. In list I some straight line corresponding signs of slopes he straight lines graphs are given and in i es and intercepts are given ch the type of graphs of list I corresponding to sign of slopes and intercepts in list List I (D) T (C) 4 List II (i) Positive slopez (iii) Positive intercept (v) Zero intercept (ii) Negative slope (iv) Negative intercept (vi) Zero slope | 11 |

580 | In uniform circular motion, the velocity vector and acceleration vector are: A. perpendicular to each other B. in the same direction c. opposite in direction D. not related to each other | 11 |

581 | 19. During a projectile motion, if the maximum height equals the horizontal range, then the angle of projection with the horizontal is a. tan-‘(1) b. tan-‘(2) c. tan-‘(3) d. tan-(4) | 11 |

582 | Three particles ( A, B ) and ( C ) are situated at the vertices of an equilateral triangle ABC of side d at time ( t=0 . ) Each of the particles moves with constant speed v. A always has its velocity along ( mathrm{AB}, mathrm{B} ) along BC and ( C ) along CA. At what time will the particles meet each other? A ( cdot frac{2 d}{3 v} ) в. ( frac{3 d}{2 v} ) c. ( frac{4 d}{3 v} ) D. ( frac{3 d}{4 v} ) | 11 |

583 | The radius of the blade of fan is ( 0.3 mathrm{m} ). It is making 1200 rev/min.The acceleration of a particle at the tip of the blade is: A ( cdot 3733 m / s^{2} ) В. ( 2733 m / s^{2} ) c. ( 4733 m / s^{2} ) D. ( 5733 m / s^{2} ) | 11 |

584 | A maglev train is gradually taking a ( 45^{circ} ) turn while moving with constant-speed of ( pi m s^{-1} . ) For a special compartment of train, turning process takes ( 220 m ) length on the track. Magnitude of centripetal acceleration of the train is: A cdot Is constant and ( frac{pi}{88} m s^{-2} ) (approximately) B. Is variable c. zero, as speed is constant D. Either (2) or (3) | 11 |

585 | A block of mass ( m=1 k g ) has speed ( v=4 m / s ) at ( theta=60^{circ} ) on a circular track of radiu ( R=2 m ) as shown in figure. Coefficient of kinetic friction between the block and the track is ( mu_{k}=0.5 ) tangential acceleration of the block at this instant is approximately. A ( .2 .1 m / s^{2} ) В ( cdot 5 m / s^{2} ) ( mathrm{c} cdot 1.2 mathrm{m} / mathrm{s}^{2} ) D. ( 3 m / s^{2} ) | 11 |

586 | Fig. 5.208 12. The vertical component of the velocity of block at A is a. 3 b. 2/8 c. 3/ d. 48 | 11 |

587 | A particle is projected up an inclined plane of inclination ( beta ) at an elevation a to the horizon. Show that a. ( tan alpha+cot beta+2 tan beta, ) if the particle strikes the plane at right angles b. ( tan alpha=2 tan beta ) if the particle strikes the plane horizontally. | 11 |

588 | A motorboat is racing towards the north at ( 25 k m h^{-1} ) and the water current in that region is ( 10 mathrm{kmh}^{-1} ) in the direction of ( 60^{circ} ) east of south. The resultant velocity of the boat is: ( mathbf{A} cdot 11 mathrm{kmh}^{-1} ) B . 22 ( k m h^{-1} ) c. ( 33 mathrm{kmh}^{-1} ) D. ( 44 mathrm{kmh}^{-1} ) | 11 |

589 | A man in a car at location ( Q ) on a straight highway is moving with speed ( boldsymbol{v} . ) He decides to reach a point ( boldsymbol{P} ) in a field at a distance ( boldsymbol{d} ) from highway (point ( M) ) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance ( R M, ) so that the time taken to reach P is minimum? A ( cdot frac{d}{sqrt{3}} ) B. ( d ) ( overline{2} ) c. ( frac{d}{sqrt{2}} ) D. | 11 |

590 | Assertion In case of a projectile, the angle between velocity and acceleration changes from point to point. Reason Because its horizontal component of velocity remains constant, while vertical component of velocity changes from point to point due to gravitational acceleration. A. Both Assertion and Reason are true and the Reason is correct explanation of the Assertion. B. Both Assertion and Reason are true, but Reason is not correct explanation of the Assertion. c. Assertion is true, but the Reason is false D. Assertion is false, but the Reason is true. | 11 |

591 | be ical to keep ms, and find 18. A man holds an umbrella at 30° with the vertical to himself dry. He, then, runs at a speed of 10 ms, an the rain drops to be hitting vertically. Study the follow statements and find the correct options. i. Velocity of rain w.r.t. Earth is 20 ms- ii. Velocity of rain w.r.t. man is 10/3 ms! iii. Velocity of rain w.r.t. Earth is 30 ms! iv. Velocity of rain w.r.t. man is 10/2 ms- a. Statements (i) and (ii) are correct. b. Statements (i) and (iii) are correct. c. Statements (iii) and (iv) are correct. d. Statements (ii) and (iv) are correct. D . | 11 |

592 | The acceleration experienced by a moving boat after its engine is cut-off, of given by: ( a=-k v^{3} ) where ( k ) is a constant. If ( v_{0} ) is the magnitude of velocity at cut-off, then the magnitude of the velocity at time ( t ) after the cut-off is :- A ( cdot frac{v_{0}}{2 k t v_{0}^{2}} ) В. ( frac{v_{0}}{1+2 k t v_{0}^{2}} ) c. ( frac{v_{0}}{sqrt{1-2 k t v_{0}^{2}}} ) D. ( frac{v_{0}}{sqrt{1+2 k t v_{0}^{2}}} ) | 11 |

593 | An object is moving in the ( x-y ) plane with the position as a function of time ( operatorname{given} operatorname{by} vec{r}=x(t) hat{i}+y(t) hat{j} . ) Point ( O ) is at ( boldsymbol{x}=mathbf{0}, boldsymbol{y}=mathbf{0 .} ) The object definitely moving towards 0 when A ( cdot v_{x}>0, v_{y}>0 ) 0 B ( cdot v_{x}<0, v_{y}<0 ) ( mathbf{c} cdot x v_{x}+y v_{y}0 ) | 11 |

594 | Consider the diagram of the trajectory of a thrown tomato. At what point is the potential energy greatest? | 11 |

595 | 19. At the highest point of its trajectory u² cos²0 √3u² cos² e 28 u² cos²0 a √3 u² cos²0 b. – 28 | 11 |

596 | 8. The horizontal distance between two bodies, when their velocity are perpendicular to each other, is a. I m b . 0.5 m c. 2 m d. 4 m | 11 |

597 | Rain is falling vertically with a speed of ( 20 m / s . ) After sometime wind starts blowing with a speed of ( 12 m / s ) in east to west direction in which direction should a boy waiting at a bus stop hold his umbrella. | 11 |

598 | 8. A launch travels across a river from a point A to a point B of the opposite bank along the line AB forming angle a with the bank. The flag on the mast of the launch makes an angle ß with its direction of motion. Determine the speed of the launch w.r.t. the bank. The velocity of wind is u perpendicular to the stream. Δα A Fig. 5.188 | 11 |

599 | 14. The time taken by the block to move from A to C is Ve b at . 14v3 V8 | 11 |

600 | If the frequency of the particle performing circular motion increases from 60 rmp to 180 rpm is 20 seconds, its angular acceleration is A ( cdot 0.1 mathrm{rad} / mathrm{s}^{2} ) B. 3.142 ( r a d / s^{2} ) c. 0.6284 rad ( / s^{2} ) D. 0.3142 rad/s ( ^{2} ) | 11 |

601 | A ball projected from the ground at a certain angle has: A. minimum velocity at the point of projection and maximum velocity at the maximum height B. maximum velocity at the point of projection and minimum velocity at the maximum height C. same velocity at any point in its path D. zero velocity at the maximum height irrespective of the velocity of projection | 11 |

602 | Two vectors whose magnitudes are in ratio 1: 2 gives resultant of magnitude 30. If angle between these two vectors is ( 120^{circ}, ) then the magnitude of two vectors will be A. ( 10 sqrt{3}, 20 sqrt{3} ) 3 B . ( 5 sqrt{3}, 10 sqrt{3} ) D. ( 2 sqrt{3}, 4 sqrt{3} ) | 11 |

603 | 73. A body is moving in a circular path with a constant speed. It has a. A constant velocity b. A constant acceleration c. An acceleration of constant magnitude d. An acceleration which varies with time in magnitude A 1 1 with uniform | 11 |

604 | A stationary wheel starts rotating about its own axis with an angular acceleration of 5.5 rad ( / s^{2} . ) To acquire an angular velocity 420 revolutions per minute, the number of rotations made by the wheel is: A . 14 B . 21 ( c cdot 28 ) D. 35 | 11 |

605 | Identify the direction of the angular velocity vector for the second hand of a clock going from 0 to 60 seconds? A. Outward from the clock face B. Inward toward the clock face D. Downward E. To the right | 11 |

606 | Illustration 5.75 Two particles A and B are moving as shown in Fig. 5.158. At this moment of time, find the angular speed of A relative to B. | 11 |

607 | A man in a minivan rounds a circular turn at a constant speed. Which of the following would cause the | 11 |

608 | The path followed by a projectile is called its: A. trajectory B. range c. amplitude D. none of these | 11 |

609 | A ball in thrown from a roof top at an angle ( 45^{circ} ) above the horizontal. It hits the ground a few second later. At what point during its motion, does the ball have greatest acceleration? | 11 |

610 | Assertion Linear momentum of a body changes even when it is moving uniformly in a circle. Reason In uniform circular motion velocity remains constant. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

611 | A bus is moving with a speed of ( 10 mathrm{ms}^{-1} ) on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of ( 1 mathrm{km} ) from the scooterist, with what speed should the scooterist chase the bus? A. ( 40 mathrm{ms}^{-1} ) B. 25 ( m s^{-1} ) ( mathrm{c} cdot 10 mathrm{ms}^{-1} ) D. ( 20 mathrm{ms}^{-1} ) | 11 |

612 | A body is moving along a straight line. Its distance ( X_{t} ) from a point on its path at a time ( t ) after passing that point is given by ( X_{t}=8 t^{2}-3 t^{3}, ) where ( X_{t} ) is in meter and ( t ) is in second. The correct statement(s) is/are: This question has multiple correct options A. Average speed during the interval ( t=0 ) s to ( t=4 s ) is ( 20.21 mathrm{ms}^{-1} ) B. Average velocity during the interval ( t=0 ) s to ( t=4 s ) is ( -16 m s^{-1} ) C. The body starts from rest and at ( t=frac{16}{9} s ) it reverses its direction of motion at ( x_{t}=8.43 mathrm{m} ) from the start D. It has an acceleration of ( -56 mathrm{ms}^{-2} ) at ( t=4 mathrm{s} ) | 11 |

613 | U TOM U Us 10. Two forces 3 N and 2 N are at an angle o such that the resultant is R. The first force is now increased to 6 N and the resultant become 2R. The value of O is (a) 30° (b) 60° (c) 90° (d) 120° | 11 |

614 | Which one of the following is most probably not a case of uniform circular motion? A. Motion of a racing car on a circular track B. Motion of the moon around the earth c. Motion of a toy train on a circular track D. Motion of seconds hand on the circular dial of a watch | 11 |

615 | 1. The shortest distance between the motorcyclist and the car is a. 10 m b. 20 m c . 30 m d. 40 m | 11 |

616 | Illustration 5.4 At what angle should a projectile be thrown such that the horizontal range of the projectile will be equal to half of its maximum value? | 11 |

617 | In uniform linear motion, the speed and velocity are A. Constant B. Variable c. zero D. All | 11 |

618 | If it turns an angle of ( y ) rad in these ( 3 s ) then ( 2 y ) is equal to ( 250+x ). Find ( x ) | 11 |

619 | If ( bar{a}=hat{i}-hat{j}+hat{k} ) and ( bar{b}=2 hat{i}-hat{j}+3 hat{k} ) then the unit vector along ( bar{a}+bar{b} ) is A ( cdot frac{3 hat{i}+4 hat{k}}{5} ) B. ( frac{-3 hat{i}+4 hat{k}}{5} ) c. ( frac{-3 hat{i}-4 hat{k}}{5} ) D. none of these | 11 |

620 | The relation ( 3 t=sqrt{3 x}+6 ) describes the displacement of a particle in one direction where ( x ) is in meters and ( t ) in seconds. The displacement when velocity is zero is: A ( .24 m ) B. ( 12 m ) ( c .5 m ) D. zero | 11 |

621 | 7. Two particles are projected from the same point with the same speed at different angles e, & e, to the horizontal. They have the same range. Their times of flight are t,& t2 respectively. (a) 1 = tan²0, (b) 11 = 12 sin e, cos 2 t1 = tan , (d) 1 = tan? Q2 | 11 |

622 | A stone tied to the end of a string ( 80 mathrm{cm} ) long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, the magnitude of acceleration is : A ( cdot 20 m s^{-2} ) В ( cdot 12 m / s^{2} ) c. ( 27.53 m s^{-2} ) ( mathbf{D} cdot 8 m s^{-2} ) | 11 |

623 | 16. The vertical component of the velocity of projectile is a. 3v sin o b. v sine c. vsin d v sin 12 3 | 11 |

624 | If the magnitude of its angular speed at ( boldsymbol{t}=mathbf{3 . 0 s} ) is ( boldsymbol{x} boldsymbol{r} boldsymbol{a} boldsymbol{d} / boldsymbol{s}, ) find ( boldsymbol{2} boldsymbol{x} ) | 11 |

625 | Six particles situated at the corners of a regular hexagon of side ( a ) move at a constant speed ( v ). Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet each other. A ( cdot frac{2 a}{3 v} ) в. ( frac{v}{a} ) c. ( frac{2 a}{v} ) D. ( frac{a}{3 v} ) | 11 |

626 | A ship ( A ) is moving Westwards with a speed of ( 10 mathrm{km} h^{-1} ) and a ship ( mathrm{B} 100 mathrm{km} ) South of ( A ) is moving northwards with a speed of ( 10 mathrm{km} h^{-1} ). The time after which the distance between them becomes shortest is ( mathbf{A} cdot 0 h ) в. ( 5 h ) c. ( 5 sqrt{2} h ) D. ( 10 sqrt{2} h ) | 11 |

627 | A body crosses the topmost point of a vertical circle with critical speed. What will be its centripetal acceleration when the string is horizontal: ( mathbf{A} cdot g ) B. ( 2 g ) c. ( 3 g ) D. ( 6 g ) | 11 |

628 | Is it possible to have an accelerated motion with a constant speed? Name such type of motion A. Yes, Uniform Circular Motion B. Yes, Non-Uniform Circular Motion c. Yes, Uniform Linear Motion D. No | 11 |

629 | When two bodies approach each other with different uniform speeds, the distance between them decreases by ( 120 m ) per every 1 min. If they move in the same direction, the distance between them increases by ( 90 m ) per every 1 min. The speeds of the bodies are respectively. A ( .2 m / s, 0.5 m / s ) B. ( 3 m / s, 2 m / s ) c. ( 1.75 m / s, 0.25 m / s ) D. ( 2.5 m / s, 0.5 m / s ) | 11 |

630 | Two particles projected from the same point with same speed ( u ) at angles of projection ( alpha ) and ( beta ) strike the horizontal ground at the same point. If ( boldsymbol{h}_{1} ) and ( boldsymbol{h}_{mathbf{2}} ) are the maximum heights attained by the projectile, ( boldsymbol{R} ) is the range for both ( boldsymbol{t}_{1} ) and ( t_{2} ) are their times of flights, respectively, then This question has multiple correct options ( mathbf{A} cdot alpha+beta=frac{pi}{2} ) B . ( R=4 sqrt{h_{1} h_{2}} ) c. ( frac{t_{1}}{t_{2}}=tan alpha ) D ( cdot tan alpha=sqrt{frac{h_{1}}{h_{2}}} ) | 11 |

631 | A ball is moving with speed ( 20 mathrm{m} / mathrm{s} ) collides with a smooth surface as shown in figure. The magnitude of change in velocity of the ball will be (Smooth horizontal surface) ( mathbf{A} cdot 10 sqrt{3} mathrm{m} / mathrm{s} ) B. ( 20 sqrt{3} mathrm{m} / mathrm{s} ) ( c cdot frac{40}{sqrt{3}} m / s ) D. ( 40 mathrm{m} / mathrm{s} ) | 11 |

632 | How does uniform circular motion differ from uniform linear motion? | 11 |

633 | A particle is moving along a fixed circular orbit with uniform speed. Then the correct statement among the following is: A. Angular momentum of particle is constant only in magnitude but its direction changes from point to point B. Angular momentum of particle is constant only in direction but its magnitude changes from point to point C. Angular momentum of particle is constant both in magnitude and direction D. Angular momentum of particle is not constant both in magnitude and direction | 11 |

634 | 10 u. 20 S shot is fired at an angle to the horizontal such that it strikes the hill while moving horizontally. Find the initial angle of projection 0. 370 Fig. 6.25 a. tan = b. tan e = 3 c. tan 0 = = d. None of these | 11 |

635 | Which parameters shown below are common between uniform circular motion and uniform linear motion A. Velocity B. Speedd c. Displacement D. Acceleration | 11 |

636 | Two masses are connected by a spring as shown in the figure. One of the masses was given velocity ( v=2 k ) as shown in figure where ( k ) is the spring constant. Then maximum extension in the spring will be? (initially spring is in natural length) A . 2 m в. ( m ) ( mathrm{c} cdot sqrt{2 m k} ) D. ( sqrt{3 m k} ) | 11 |

637 | Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity ( boldsymbol{v} ) and other with a uniform acceleration ( a . ) If ( alpha ) is the angle between the lines of motion of two particles then the least value of relative velocity will be at time given by B. ( (v / a) cos alpha ) ( mathbf{D} cdot(v / a) cot alpha ) | 11 |

638 | 8. A car moves on a circular road describing equal angles about the centre in equal intervals of time. Which of the following statements about the velocity of car are not true? a. Velocity is constant. b. Magnitude of velocity is constant but the direction changes. c. Both magnitude and direction of velocity change. d. Velocity is directed towards the center of circle. | 11 |

639 | Assertion A particle has constant acceleration is x-y plane. But neither of its acceleration components ( left(a_{x} text { and } a_{y}right) ) is zero. Under this condition particle can not have parabolic path. Reason In projectile motion, horizontal component of acceleration is zero. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

640 | A man can row a boat with ( 4 k m / h ) in still water. If he is crossing a river where the current is ( 2 k m / h . ) Width of river is 4 k ( m ). In what direction should he head the boat if he wants to cross the river in shortest time and what is this minimum time? A. Parallel to river current, 2 hrs B. Perpendicular to river current, 2 hrs C. Parallel to river current, 1 hrs D. Perpendicular to river current, 1 hrs | 11 |

641 | On the application of a constant torque, a wheel is turned from rest through 400 radian in ( 10 s . ) Calculate its angular acceleration. ( left(operatorname{in} r a d / s^{2}right) ) A . 8 B. 9 ( c cdot 4 ) D. | 11 |

642 | ** * * * 1. Just as the student starts his free fall, he presses the button of the stopwatch. When he reaches at the top of 100th floor, he has observed the reading of stopwatch as 00:00:06:00 (hh: mm: ss: 100th part of the second). Find the value of 8. (Correct up to two decimal places) a. 10.00 ms-2 b. 9.25 ms-2 c. 9.75 ms-2 d. 9.50 ms 2 | 11 |

643 | 16. If Tin the total time of flight, h is the maximum height and R is the range for horizontal motion, the x and y co ordinates of projectile motion and time t are related as .. (-) -an)–) 6. -a-(1)-1) . =an(*)(* = 5) | 11 |

644 | Between ( t=10 ) s and ( t=20 s, ) the merry-go-round. A. rotates clockwise, at a constant rate B. rotates clockwise, and slows down C. rotates counterwise, at a constant rate D. rotates counterclockwise, and slows, down | 11 |

645 | Two force ( 5 k g-w t . ) And ( 10 k g-w t ) are acting with an inclination of ( 120^{circ} ) between them. Find the angle when the resultant marks with ( 10 k g-w t ) | 11 |

646 | A body tied to a string of length Lis revolved in a vertical circle with minimum velocity, when the body reaches the upper most point the string breaks and the body moves under the influence of the gravitational field of earth along a parabolic path. The horizontal range ( A C ) of the body will be: A ( . x=L ) В . ( x=2 L ) c. ( x=2 sqrt{2 L} ) D. ( x=sqrt{2 L} ) | 11 |

647 | VI “PIO I SUS. 24. Two particles start moving simultaneously with constant velocities u, and uz as shown in Fig 5.194. First particle starts from A along AO and second starts from O along OM. Find the shortest distance between them during their motion. N xo Fig. 5.194 | 11 |

648 | A particle is moving along a circular path of radius ( 5 m ) with a uniform speed ( 5 m s^{-1} . ) What will be the average acceleration when the particle completes half revolution? A. Zero B. ( 10 mathrm{ms}^{-2} ) ( mathbf{c} cdot 10 pi mathrm{ms}^{-2} ) D. ( frac{10}{pi} m s^{-2} ) | 11 |

649 | The equation of projectile is ( y=16 x- ) ( frac{5 x^{2}}{4} ) Find the horizontal range. ( mathbf{A} cdot R=13.8 m ) В. ( R=8 m ) c. ( R=12.8 mathrm{m} ) D. ( R=9 m ) | 11 |

650 | A train of ( 150 mathrm{m} ) length is going towards north direction at a speed of ( 10 mathrm{ms}^{-1} . mathrm{A} ) parrot flies at a speed of ( 5 m s^{-1} ) towards south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to: A . 12 B. 8 s ( c cdot 15 s ) D. 10 s | 11 |

651 | A wheel completes 2000 revolutions to cover the ( 9.5 mathrm{km} ) distance, then the diameter of the wheel is A . ( 1.5 mathrm{m} ) B. ( 1.5 mathrm{cm} ) c. ( 7.5 mathrm{cm} ) D. 7.5 ( m ) | 11 |

652 | The product of two vectors ( vec{A} ) and ( vec{B} ) may be: This question has multiple correct options ( mathbf{A} cdot geq A B ) в. ( leq A B ) c. ( <A B ) D. zero | 11 |

653 | The horizontal range of a projectile fired at an angle of ( 15^{circ} ) is ( 50 mathrm{m} ). If it is fired with the same speed at an angle of ( 45^{circ} ) its range will be: A. ( 60 mathrm{m} ) B. 71 c. ( 100 mathrm{m} ) D. ( 141 mathrm{m} ) | 11 |

654 | A blue car rounds a circular turn at a constant speed of ( 30 m / s . ) A grey van rounds the same turn at a constant speed of ( 15 m / s . ) How does the magnitude of the acceleration of the blue car compare to the magnitude of the acceleration of the grey van? A. The accelerations of both vehicles are zero, since neither is changing speed B. The magnitude of the blue car’s acceleration is twice the magnitude of the grey van’s acceleration c. The magnitude of the blue car’s acceleration is four times the magnitude of the grey van’s acceleration D. The magnitude of each car’s acceleration is the same, but is not zero E. We do not have enough information to determine the relative magnitudes of acceleration for the cars in this questions | 11 |

655 | 21. In going from one city to another, a car travels 75 km north, 60 km north-west and 20 km east. The magni- tude of displacement between the two cities is (take 1/2 = 0.7) a. 170 km b. 137 km c. 119 km d. 140 km | 11 |

656 | A fighter plane flying horizontally at an altitude of ( 1.5 k m ) with speed ( 720 k m / h ) passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 ms( ^{-1} ) to hit the plane ? At what minimum altitude should the pilot fly the plane to avoid being hit ? Take ( g=10 m s^{-2} ) | 11 |

657 | Two vectors ( X ) and ( Y ) are added together. Which of the following statements could be true? I. The resultant magnitude is smaller than X. II. The resultant magnitude is larger than ( Y ) III. The resultant direction is the same as either ( X ) or ( Y ) A. I only B. II only C. I and III only D. II and III only E . ।, ॥।, and III | 11 |

658 | A centrifuge starts rotating from rest and reaches a rotational speed of 8,000 radians/sec in 25 seconds. Calculate the angular acceleration of the centrifuge? A. 160 radians ( / )sec( ^{2} ) B. 320radians/sec^ c. 640 radians / sec ( ^{2} ) D. 10,000 radians ( / )sec( ^{2} ) E .20,000 radians / sec ( ^{2} ) | 11 |

659 | In uniform circular motion, direction of velocity goes on changing continuously, however the magnitude of velocity is constant. A. True B. False | 11 |

660 | 8. In Fig. A.46, find the horizontal velocity u (in ms-l) of a projectile so that it hits the inclined plane perpendicularly. Given H = 6.25 m. 30° A ialiniated from a static | 11 |

661 | 5. The path of a projectile in the absence of air drag is shown in the figure by dotted line. If the air resistance is not ignored then which one of the path shown in the figure is appropriate for the projectile A B C D (a) B (b) A (c) D (d) c . | 11 |

662 | with a velocity of 5 ms. The 1. A river is flowing towards with a velocity 01 boat velocity is 10 ms. The boat crosses the river by shortest path. Hence, a. The direction of boat’s velocity is 30° west of b. The direction of boat’s velocity is north-west. c. Resultant velocity is 53 ms. d. Resultant velocity of boat is 5/2 ms. | 11 |

663 | The position vector of a particle ( vec{R} ) as a function of time is given by: ( overrightarrow{boldsymbol{R}}=boldsymbol{4} sin (2 pi t) hat{hat{i}}+4 cos (2 pi t) hat{j} ) where ( R ) is in meters, ( t ) is in seconds and ( hat{i} ) and ( hat{j} ) denote unit vectors along ( x ) and y- directions, respectively. Which one of the following statements is wrong for the motion of particle? A. Path of the particle is a circle of radius ( 4 mathrm{m} ) B. Acceleration vector is along ( -vec{R} ). C. Magnitude of acceleration vector is ( frac{v^{2}}{R} ), where ( v ) is th velocity of particle D. Magnitude of the velocity of particle is ( 8 mathrm{m} / mathrm{s} ) | 11 |

664 | Write down a unit vector in ( X Y ) – plane, making an angle of ( 30^{circ} ) with the positive direction of ( boldsymbol{x} ) – axis. | 11 |

665 | For a particle performing uniform circular motion, choose the incorrect statement from the following. A. Magnitude of particle velocity (speed) remains constant B. Particle velocity remains directed perpendicular to radius vector c. Direction of acceleration keeps changing as particle moves D. Magnitude of acceleration does not remain constant | 11 |

666 | The maximum height attained by a projectile is found to be equal to 0.433 of horizontal range. The angle of projection of this projectile is A ( .30^{circ} ) В ( cdot 45^{circ} ) ( c cdot 60^{0} ) D. ( 75^{circ} ) | 11 |

667 | A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rev/sec in 4 seconds.Find the angular acceleration. Find the angle rotated during these four seconds. | 11 |

668 | 15. Twelve persons are initially at 12 corners of a regular polygon of 12 sides of side a. Each person now moves with a uniform speed v in such a manner that 1 is always directed towards 2, 2 towards 3, 3 towards 4, and so on. The time after which they meet is a. La – b. b. – 2a 2a c. v(2+√3) d. v(2-√3) | 11 |

669 | A thin circular loop of radius R rotates about its vertical diameter with an angular frequency ( omega . ) Show that a small bead on the wire loop remains at its lower most point for ( omega leq sqrt{g / R} ). What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for ( omega= ) ( sqrt{2 g / R} ? ) Neglect friction. | 11 |

670 | If a particle is kept at rest at origin, another particle starts from (5,0) with a velocity of ( -4 hat{i}+3 hat{j} ). Find their closest distance of approach. ( A .3 m ) в. ( 4 m ) ( c .5 m ) D. ( 2 m ) | 11 |

671 | A police jeep is chasing with velocity of ( 45 k m / h ) a thief in another jeep moving with velocity ( 153 k m / h . ) Police fires a bullet with muzzle velocity of ( 180 m / s ) The velocity it will strike the car of the thief is? A. ( 150 mathrm{m} / mathrm{s} ) в. ( 27 mathrm{m} / mathrm{s} ) c. ( 450 m / s ) D. ( 250 mathrm{m} / mathrm{s} ) | 11 |

672 | 59. A particle is moving in the x-y plane. At certain instant of time, the components of its velocity and acceleration are as follows: v; = 3 ms-, v = 4 ms’, az = 2 ms and a, = 1 ms. The rate of change of speed at this moment is a. V10 ms 2 b. 4 ms-2 c. 15 ms-2 d. 2 ms-2 | 11 |

673 | ct is projected with a velocity of 20 m/s making an OI 45° with horizontal. The equation for the trajectory is h = Ax – Bx2 where his height, x is horizonta A and B are constants. The ratio A:B is (g = 10 ms) (a) 1:5 (b) 5:1 (c) 1:40 (d) 40:1 onge R for | 11 |

674 | Two runners start simultaneously from the same point on a circular ( 200 m ) track in the same direction. Their speeds are ( 6.2 m s^{-1} ) and ( 5.5 m s^{-1} . ) How far from the starting point the faster and the slower runner would be side by side again? A. ( 150 mathrm{m} ) away from the starting point B. ( 170 m ) away from the starting point c. ( 120 m ) away from the starting point D. none | 11 |

675 | A solid body starts rotating about a stationary axis with an angular acceleration ( boldsymbol{alpha}=left(mathbf{2 . 0} times mathbf{1 0}^{-mathbf{2}}right) boldsymbol{t} boldsymbol{r a d} / boldsymbol{s}^{2} ) where ( t ) is in seconds. How soon(in seconds) after the beginning of rotation will the total acceleration vector of an arbitrary point of the body form an angle ( boldsymbol{theta}=mathbf{6 0}^{circ} ) with its velocity vector? | 11 |

676 | A body ties to a string of length ( boldsymbol{L} ) is revolved in a vertical circle with minimum velocity, when the body reaches the upper most point the string breaks and the body moves under the influence of the gravitational field of earth along a parabolic path. The horizontal range ( A C ) of the body will be: A ( . x=L ) B. ( x=2 L ) C ( . x=2 sqrt{2 L} ) ( mathbf{D} cdot x=sqrt{2 L} ) | 11 |

677 | The figure represents a displacement time graph of a body moving in a straight line. The instantaneous velocity of the body at ( 3 s ) is : A ( cdot 4 m s^{-1} ) B. ( 3 m s^{-1} ) ( c ) D. ( 1 mathrm{ms}^{-1} ) | 11 |

678 | The formula ( v=R omega ) relating linear and angular velocity is true, only if A. The velocities are instantaneous velocities B. The velocities are average velocities c. The velocities are initial velocities and the particle is moving with constant acceleration D. The velocities are initial velocities and the particle is moving with constant retardation | 11 |

679 | The force on a particle of mass 10 g is ( (10 hat{i}+5 hat{j}) N . ) if it starts from rest, what would be its position at time ( t=5 s ? ) A . ( 12500 hat{i}+6250 hat{j} mathrm{m} ) B. 6250hat ( +12500 hat{j} mathrm{m} ) c. ( 12500 hat{i}+12500 hat{j} mathrm{m} ) D. 6250hat + 6250hat m | 11 |

680 | When a force ( F_{1} ) acts on a particle, frequency ( 6 mathrm{Hz} ) and when a force ( F_{2} ) acts frequency is 8 Hz. What is the frequency when both the force act simultaneously in same direction? A . 12 нᅩ в. 25нд с. 10 н D. ( 5 mathrm{Hz} ) | 11 |

681 | Driver of a train travelling at ( 115 k m / h ) sees on a same track, ( 100 m ) infront of him, a slow train travelling in the same direction at ( 25 k m / h ). The least retardation that must be appiled to faster train to avoid a collision is A. ( 3.125 mathrm{m} / mathrm{s}^{2} ) в. ( 3.5 m / s^{2} ) ( mathbf{c} cdot 2.75 m / s^{2} ) D. ( 3.0 m / s^{2} ) | 11 |

682 | A projectile at any instant during its flight has velocity ( 5 ~ m / s ) at ( 30^{circ} ) above the horizontal. How long after this instant, will it be moving at right angle to the given direction? | 11 |

683 | A train of length ( 100 m ) is moving in a hilly region. At what speed must it approach a tunnel of length ( 80 m ) so that a person at rest with respect to the tunnel will see that the entire train is in the tunnel at one time? A. ( 1.25 c ) B. ( 0.8 c ) c. ( 0.64 c ) D. ( 0.6 c ) E ( .0 .36 c ) | 11 |

684 | You spin a globe at 2.5 rads/sec and then give it a push to speed it up to 3 rads/ sec. If it takes 0.2 secs to change the speed of the globe, what is the angular acceleration in ( r a d / s e c^{2} ? ) A . 2.5 B. 3 ( c cdot 5 ) D. 10 | 11 |

685 | 5un. 15 10 10 ) 34. A particle is projected up an inclined plane of inclination B at an elevation a to the horizon. Show that a. tan a=cot B+ 2 tan B, if the particle strikes the plane at right angles b. tana = 2 tan B, if the particle strikes the plane horizontally 25 T L 1: lined to the horizon | 11 |

686 | A boy standing on a long railroad car throws a ball straight upwards. The car is moving on the horizontal road with an acceleration of ( 1 mathrm{ms}^{-2} ) and the projection velocity in the vertical direction is ( 9 cdot 8 m s^{-2} . ) How far behind the boy will the ball fall on the car? | 11 |

687 | (I JUL, 1J) 2. Four persons K, L, M, N are initially at the four corners of a square of side d. Each person now moves with a uniform speed v in such a way that K always moves directly towards L, L directly towards M, M directly towards N, and N directly towards K. The four persons will meet at a time (IIT JEE, 1984) | 11 |

688 | The projection of the vector ( A=hat{i}-2 hat{j}+ ) ( hat{k} ) on the vector ( mathrm{B}=4 hat{i}-4 hat{j}+7 hat{k} ) is: A . ( 19 / 9 ) в. 38/9 ( c cdot 8 / 9 ) ( D cdot 4 / 9 ) | 11 |

689 | A train of length ( 50 m ) is moving with a constant speed of ( 10 m / s . ) Calculate the time taken by the train to cross an electric pole and a bridge of length ( mathbf{2 5 0 m} ) | 11 |

690 | The maximum and the minimum magnitude of the resultant two vectors are 17 and 7 units respectively. Then the magnitude of the resultant vector when they act perpendicular to each other is: A . 14 B. 16 c. 18 D. 13 | 11 |

691 | 1. If a particle moves from point P (2,3,5) to point Q (3,4,5). Its displacement vector be (a) i + i +10k (b) î + i +5k (c) i tŷ preg (d) zi +47 + 6k | 11 |

692 | unc magnitude oi A. 13. Three vectors as shown in Fig. 3.71 have magnitudes lal = 3,1b1 = 4, and lcl=10. Ty 1.90 30° 21,30 Fig. 3.71 a. Find the x and y components of these vectors. b. Find the numbers p and q such that c = pā+qb. | 11 |

693 | An aeroplane flying horizontally with speed ( 90 mathrm{km} / mathrm{hr} ) releases a bomb at a height of ( 78.4 mathrm{m} ) from the ground, when will the bomb strike the ground? A. 8 sec B. 6 sec c. 4 sec D. 10 sec | 11 |

694 | A particle is projected from ground with velocity ( 40 sqrt{2} m / s a t 45^{circ} . ) Find the displacement of the particle after 2 s. ( left(g=10 m / s^{2}right) ) | 11 |

695 | Is the claim of Mr.Kirkpatrick right? A . yes B. No c. cannot say D. may be correct or may be not | 11 |

696 | 11. Two forces of magnitudes P and Q are inclined at an angle (O). The magnitude of their resultant is 3Q. When the inclination is changed to (180° – 0), the magnitude of the resultant force becomes Q. Find the ratio of the forces. | 11 |

697 | average velocity, | 11 |

698 | What is the equation of parabolic trajectory of a projectile? ( (boldsymbol{theta}= ) angle between the projectile motion and the horizontal) A ( cdot y=x^{2} tan theta-frac{g x}{2 u^{2} cos ^{2} theta} ) B. ( y=x tan theta-frac{g x^{2}}{2 u^{2} cos ^{2} theta} ) c. ( y=x tan theta-frac{g x^{2}}{u^{2} cos 2 theta} ) D. ( y=x tan theta-frac{g x^{2}}{u^{2} sin ^{2} theta} ) | 11 |

699 | Is the acceleration of a particle in uniform circular motion constant or variable? A. Variable B. Constant c. Sometimes constant D. Always constant | 11 |

700 | single Correct Answer Type The path of a projectile is given by the equation ( y=a x-b x^{2}, ) where ( a ) and ( b ) are constants and ( x ) and ( y ) are respectively horizontal and vertical distances of projectile from the point of projection. The maximum height attained by the projectile and the angle of projection are respectively: A ( cdot frac{2 a^{2}}{b}, tan ^{-1}(a) ) B. ( frac{b^{2}}{2 a}, tan ^{-1}(b) ) c. ( frac{a^{2}}{b}, tan ^{-1}(2 b) ) D ( cdot frac{a^{2}}{4 b}, tan ^{-1}(a) ) | 11 |

701 | There are two force vectors, one of ( 5 N ) and other of ( 12 N . ) At what angle should the two vectors be added to get the resultant vector of ( 17 N, 7 N, ) and ( 13 N ) respectively? | 11 |

702 | Three forces of magnitudes 30,60 and ( P ) Newton acting at a point are in equilibrium. If the angle between the first two is ( 60^{circ} ), the value of ( P ) is: A ( cdot 25 sqrt{2} ) в. ( 30 sqrt{3} ) c. ( 30 sqrt{6} ) D. ( 30 sqrt{7} ) | 11 |

703 | A unit vector in the direction of vector ( overrightarrow{P Q}, ) where ( P ) and ( Q ) are the points (1,2,3) and (4,5,6) respectively is A ( cdot frac{1}{sqrt{3}} hat{i}+frac{1}{sqrt{3}} hat{j}+frac{1}{sqrt{3}} bar{k} ) B. ( frac{1}{sqrt{3}} hat{i}+frac{1}{sqrt{3}} hat{j}-frac{1}{sqrt{3}} hat{k} ) c. ( 2 hat{i}-hat{j}+bar{k} ) D. None | 11 |

704 | Two vectors ( A ) and ( B ) have equal magnitudes. If magnitude of ( A+B ) is equal to ( n ) times the magnitude of ( A-B ) then the angle between ( A ) and ( B ) is A ( cdot cos ^{-1}left(frac{n-1}{n+1}right) ) B. ( cos ^{-1}left(frac{n^{2}-1}{n^{2}+1}right) ) c. ( sin ^{-1}left(frac{n-1}{n+1}right) ) D. ( sin ^{-1}left(frac{n^{2}-1}{n^{2}+1}right) ) | 11 |

705 | 21. A ball is projected from ground with speed u, at an angle above horizontal. Let v be its speed at any moment t and s be the total distance covered by it till this moment, the correct graph(s) is/are a. 1 b. | 11 |

706 | When a ceiling fan is switched off, its angular velocity reduces to half its initial value after it completes 36 rotations. The number of rotations it will make further before coming to rest is Assuming angular retardation to be uniform A . 10 B . 20 ( c .18 ) D. 12 | 11 |

707 | The instantaneous velocity of a body can be measured :- A. Graphically B. By speedometer c. Both of above D. vectorially | 11 |

708 | On a foggy day, two drivers spot in front of each other when 80 metre apart. They were traveling at ( 70 mathrm{kmph} ) and ( 60 mathrm{kmph} ) Both apply brakes simultaneously which retard the cars at the rate ( 5left[boldsymbol{m} / boldsymbol{s}^{2}right] ) Which of the following statements is correct? A. The collision will be averted B. The collision will take place c. They will across each other D. They will just collide | 11 |

709 | Six particles situated at the corners of a regular hexagon of side a move at a constant speed v. Each particle maintains a direction towards the particle at the next corner. If the time taken by the particles to meet each other is ( frac{n a}{v} . ) Then ( n ) is given by | 11 |

710 | Find the radius and energy of a ( H e^{+} ) ion in the state ( n=4 ) | 11 |

711 | Find how the total acceleration ( omega ) of the balloon depends on the height of ascent. A. ( omega=2 a v_{0} ) B. ( omega=-2 a v_{0} ) c. ( omega=a v_{0} ) D. ( omega=-a v_{0} ) | 11 |

712 | What is the angle between ( vec{P} ) and the resultant of ( (vec{P}+vec{Q}) ) and ( (vec{P}-vec{Q}) ? ) A. zero в. ( tan ^{-1} frac{P}{Q} ) c. ( tan ^{-1} frac{Q}{P} ) D. ( tan ^{-1}left(frac{P-Q}{P+Q}right) ) | 11 |

713 | A rope is wound around a hollow cylinder of mass ( 3 k g ) and radius ( 40 c m ) What is the angular acceleration of the cylinder if the rope is pulled with a force of ( 30 N ? ) ( mathbf{A} cdot 5 m / s^{2} ) B . ( 25 mathrm{m} / mathrm{s}^{2} ) c. ( 0.25 mathrm{rad} / mathrm{s}^{2} ) ( mathbf{D} cdot 25 mathrm{rad} / mathrm{s}^{2} ) | 11 |

714 | What is centripetal acceleration? Drive an impression for centripetal acceleration. | 11 |

715 | A body of mass ( m ) is projected with initial speed ( u ) at an angle ( theta ) with the horizontal. The change in momentum of body after time ( t ) is A ( . m u sin theta ) B . ( 2 m u sin theta ) ( mathrm{c} cdot m g t ) D. zero | 11 |

716 | Which one of the following diagrams best represents the path followed by a projectile that has been launched horizontally from a countertop? ( A ) в. ( c ) D. | 11 |

717 | The motion of a bus going around a traffic roundabout is curvilinear motion. True or false A. True B. False | 11 |

718 | A particle moves in a circle describing equal angle in equal times, its velocity vector A. remains constant B. changes in magnitude c. change in direction D. changes in magnitude and direction | 11 |

719 | A boy of height ( 1.5 mathrm{m}, ) making move on a skateboard due east with velocity ( 4 mathrm{m} ) s ( -1, ) throws a coin vertically up with a velocity of ( 3 mathrm{m} mathrm{s}^{-1} ) relative to himself. a. Find the total displacement of the coin relative to ground till it comes to the hand of the boy. b. What is the maximum height attained by the coin w.r.t to ground? | 11 |

720 | Select incorrect statement A ( cdot ) for any two vectors ( |vec{A} cdot vec{B}| leq A B ) B. for any two vectors ( |vec{A} times vec{B}| leq A B ). C. a vector is not changed if it is slid parallel to itself. D. a vector is necessarily changed if it is rotated through an angle | 11 |

721 | 74. A particle is moving along a circular path with uniform speed. Through what angle does its angular velocity change when it completes half of the circular path? a. 0° b. 45º c. 180° d. 360° 75 Anarticle is moving along a cirenlar nath The anana | 11 |

722 | 20. Time of flight of the particle a. 8 b. 6 s c. 4s d. 2 s | 11 |

723 | A ball of mass ( m ) is projected from the ground with an initial velocity ( u ) making an angle of ( theta ) with the horizontal. What is the change in velocity between the point of projection and the highest point? A . ( u sin theta ) B . ( u^{2} cos theta ) c. ( u cos theta ) D. ( u^{2} sin theta ) | 11 |

724 | The path of a projectile is a parabola A. True B. False | 11 |

725 | Find how the tangential acceleration ( omega_{tau} ) of the balloon depends on the height of ascent. A ( cdot_{omega_{tau}}=frac{2 a^{2} y}{sqrt{1+left(frac{a y}{v_{0}}right)^{2}}} ) B. ( _{omega_{tau}}=frac{a^{2} y}{sqrt{1+left(frac{a y}{v_{0}}right)^{2}}} ) ( ^{mathbf{c}} cdot_{omega_{tau}}=frac{a^{2} y}{sqrt{1+left(frac{2 a y}{v_{0}}right)^{2}}} ) D. ( omega_{tau}=frac{a^{2} y}{2 sqrt{1+left(frac{a y}{v_{0}}right)^{2}}} ) | 11 |

726 | In one second, a particle goes from point ( A ) to point ( B ) moving in a semicircle. Find the magnitude of the average velocity. ( A cdot 1 mathrm{m} / mathrm{s} ) B. 2 m/s c. ( 0.5 mathrm{m} / mathrm{s} ) D. None of the above | 11 |

727 | A particle is projected from horizontal making an angle ( 60^{circ} ) with initial velocity ( 40 m s^{-1} . ) Find the time taken by the particle to make angle ( 45^{circ} ) from horizontal. A . ( 1.5 s ) в. 2.5 ( s ) ( c .3 .5 s ) D. 4.5 | 11 |

728 | Find a unit vector in the direction of the vector ( overrightarrow{boldsymbol{a}}=hat{boldsymbol{i}}+mathbf{2} hat{boldsymbol{j}}+mathbf{3} hat{boldsymbol{k}} ) | 11 |

729 | Assertion : When a particle moves in a circle with a uniform speed, its velocity and acceleration both changes. Reason : The centripetal acceleration in circular motion is dependent on angular velocity of the body. | 11 |

730 | The coordinates of a moving particle at time ( t ) are given by ( x=c t^{2} ) and ( y=b t^{2} ) The speed of the particle is given by A ( cdot 2 t(c+b) ) B . ( 2 t sqrt{left(c^{2}-b^{2}right)} ) c. ( t sqrt{left(c^{2}+b^{2}right)} ) D. ( 2 t sqrt{left(c^{2}+b^{2}right)} ) | 11 |

731 | Particle A and B moving in co-planar circular paths centered at O.They are rotating in the same sense.Time periods of rotation of ( A ) and ( B ) around 0 ( operatorname{are} boldsymbol{T}_{A} boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{T}_{B}, ) respectively, with ( boldsymbol{T}_{B}> ) ( T_{A} . ) Time required for ( B ) to make one rotation around 0 relative to a is : A ( cdot T_{B}-T_{A} ) в. ( T_{B}+T_{A} ) c. ( frac{T_{A} T_{B}}{T_{A}-T_{B}} ) D. ( frac{T_{B} T_{A}}{T_{B}-T_{A}} ) | 11 |

732 | U. TOJ MIS 0. A bird is flying towards north with a velocity 40 km and a train is moving with velocity 40 km h towards east. What is the velocity of the bird noted by a man in the train? a. 40/2 km h-‘N-E b. 40/2 km h-S-E c. 40/2 km h-N-W d. 40/2 km h-‘S-W | 11 |

733 | d. 2 cm along negative x-axis 10. What is the angle between two vector forces of equal magnitude such that their resultant is one-third of either of the original forces? a. cos b. cos’ (-3) d. 120° c. 45° | 11 |

734 | The velocity vector of a particle moving in the xy plane is given by ( vec{v}=t hat{i}+x hat{j} ). If initially, the particle was at origin then the equation of trajectory of the projectile is? | 11 |

735 | An aeroplane is moving in a circular path with a speed ( 250 mathrm{km} / mathrm{hr} ) in a horizontal plane. The change in magnitude of velocity in half the revolution is: A. ( 500 mathrm{km} / mathrm{hr} ) B. ( 250 mathrm{km} / mathrm{hr} ) c. ( 125 mathrm{km} / mathrm{hr} ) D. | 11 |

736 | A system is shown in the figure. Block ( boldsymbol{A} ) moves with velocity ( 10 m / s . ) The speed of the mass ( B ) will be: ( left(sin 15^{circ}=right. ) ( left.frac{sqrt{3}-1}{2 sqrt{2}}right) ) A. ( 10 sqrt{2} mathrm{m} / mathrm{s} ) в. ( 5 sqrt{3} ) m/ c. ( frac{20}{sqrt{3}} m / s ) D. ( 10 mathrm{m} / mathrm{s} ) | 11 |

737 | The force ( F ) which is applied to ( 1 k g ) block initially at rest varies linearly with time as shown in the figure. Find velocity of the block at ( t=4 s ) A ( .100 mathrm{m} / mathrm{s} ) B. ( 200 mathrm{m} / mathrm{s} ) ( c cdot 20 m / s ) D. ( 4 m / s ) | 11 |

738 | The magnitude of vector product of two vectors ( overline{mathbf{P}} times overline{mathbf{Q}} ) may be: A. equal to PQ B. less than PQ c. equal to zero D. all the above | 11 |

739 | Illustration 4.8 A particle moves along the curve =1, with constant speed v. Express its velocity vectorially as a function of (x, y). | 11 |

740 | The path of projectile is represented by y = Px – Ox’. Column I Column II L. Range a . PIQ ü. Maximum height b. P Time of flight c . P2140 Tangent of angle of d. projection is Vog | 11 |

741 | The position of an object moving along ( x ) -axis is given by ( x=a+b t^{2}, ) where ( a= ) ( 8.5 mathrm{m} ) and ( mathrm{b}=2.5 mathrm{m} mathrm{s}^{-2} ) and ( mathrm{t} ) is measured in seconds. The instantaneous velocity of the object at ( t ) ( =2 operatorname{sis} ) A ( cdot 5 mathrm{m} s^{-1} ) B. ( 10 mathrm{m} s^{-1} ) c. ( 15 mathrm{m} mathrm{s}^{-1} ) D. 20 ( mathrm{m} mathrm{s}^{-1} ) | 11 |

742 | The position vector of a particle is ( vec{r}= ) ( boldsymbol{a}[cos omega boldsymbol{t} hat{boldsymbol{i}}+sin omega boldsymbol{t} hat{j}] . ) The velocity of the particle is A. parallel to position vector B. directed towards origin c. directed away from origin D. perpendicular to position vector | 11 |

743 | A steamer is going downstream overcome a raft point ( A .2 h r ) later it turned back and after some time passed the raft at a distance ( 4 mathrm{km} ) from point ( A . ) The speed of the river is A. ( 1 mathrm{km} / mathrm{h} ) B. ( 2 mathrm{km} / mathrm{h} ) ( mathrm{c} .3 mathrm{km} / mathrm{h} ) D. ( 4 mathrm{km} / mathrm{h} ) | 11 |

744 | A particle starts from the origin at ( t=0 ) with an initial velocity of ( 3.0 hat{i} m / s ) and moves in the ( x-y ) plane with a constant acceleration ( (mathbf{6 . 0} hat{mathbf{i}}+ ) ( 4.0 hat{j}) m / s^{2} . ) The ( x- ) coordinates of the particle at the instant when its ( y- ) coordinates is ( 32 m ) is ( D ) meters. The value of ( D ) is: ( mathbf{A} .50 ) B. 60 c. 40 D. 32 | 11 |

745 | For the same two projectiles, after ( 3 s ) from the initial launch, what will be the difference between the two projectiles speeds? The previous problem’s text: A projectile is fired 30.0 degrees above the horizontal with speed ( left|boldsymbol{v}_{1}right|=mathbf{4 0 m} / boldsymbol{s} ) and a second one 60.0 degrees above the horizontal with speed ( left|boldsymbol{v}_{2}right|=mathbf{3 0 m} / boldsymbol{S} ) simultaneously. After 2 seconds, how far apart will the two projectiles be? Assume no air resistance and that they are fired from the same spot, and that each moves independent of the outer projectile. Take ( boldsymbol{g}=mathbf{9 . 8 1 m} / boldsymbol{s}^{2} ) A. ( 10 mathrm{m} / mathrm{s} ) B. ( 15.4 m / s ) c. ( 20.5 m / s ) D. ( 30.0 mathrm{m} / mathrm{s} ) E . ( 35.9 mathrm{m} / mathrm{s} ) | 11 |

746 | If ( overrightarrow{boldsymbol{A}}=mathbf{3} hat{boldsymbol{i}}-mathbf{2} hat{boldsymbol{j}}+hat{boldsymbol{k}}, overrightarrow{boldsymbol{B}}=hat{boldsymbol{i}}-boldsymbol{3} hat{boldsymbol{j}}+ ) 5 ( hat{k} a n d vec{C}=2 hat{i}+hat{j}-4 hat{k} ) form a right angled triangle then out of the following which one is satisfied? A ( cdot vec{A}=vec{B}+vec{C} )and ( A^{2}=B^{2}+C^{2} ) B . ( vec{A}=vec{B}+vec{C} )and( B^{2}=A^{2}+C^{2} ) c. ( vec{B}=vec{A}+vec{C} a n d B^{2}=A^{2}+C^{2} ) D. ( vec{B}=vec{A}+vec{C} a n d A^{2}=B^{2}+C^{2} ) | 11 |

747 | 1. In a square cut, the speed of the cricket ball changes from 30 m sto 40 ms during the time of its contact At=0.01 s with the bat. If the ball is deflected by the bat through an angle of 0 = 90°, find the magnitude of the average acceleration (in x 102ms 2) of the ball during the square cut. 11 maad | 11 |

748 | A body moves ( 6 mathrm{m} ) north. ( 8 mathrm{m} ) east and 10m vertically upwards, what is its resultant displacement from initial position (only magnitude) A ( cdot 10 sqrt{2} m ) the в. ( 10 m ) c. ( frac{10}{sqrt{2}} m ) D. ( 10 times 2 m ) | 11 |

749 | 6. A boy standing on a long railroad car throws a ball straight upwards. The car is moving on the horizontal road with an acceleration of 1 ms and the projection velocity in the vertical direction is 9.8 ms. How far behind the boy will the ball fall on the car? (in meters) | 11 |

750 | Illustration 4.1 A particle moves in the x-y plane according to the scheme x = -8 sin it and y = -2 cos 27t, where t is time. Find the equation of the path of the particle. Show the path on a graph. | 11 |

751 | 1. Rain is falling vertically downwards with a speed of 4 kmh. A girl moves on a straight road with a velocity of 3 kmh. The apparent velocity of rain with respect to the girl is a. 3 km h-‘ b. 4 kmh. c. 5 kmh’ d. 7 km h- | 11 |

752 | Find a vector of magnitude 4 units which is parallel to the vector ( sqrt{mathbf{3}} hat{mathbf{i}} ) | 11 |

753 | The given diagram shows a hill with four labelled positions ( mathrm{W}, mathrm{X}, mathrm{Y} ) and ( mathrm{Z} ) When a ball is rolled down the hill, then from which position will it finish rolling with the greatest speed? A. Position ( mathrm{w} ) B. Position ( x ) c. Position Y D. Position z | 11 |

754 | d. 1 D. 3h C. (515N U. ” 36. A juggler keeps on moving four balls in air t eeps on moving four balls in air throwing the balls after regular intervals. When one ball leaves his hand (speed = 20 ms-1), the position of other balls (height in meter) will be (take g = 10 ms) a. 10, 20, 10 . b. 15, 20, 15 c. 5, 15, 20 d. 5, 10, 20 | 11 |

755 | 12. At the highest point of the path of a projectile, its (a) speed is zero (b) speed is minimum (C) Kinetic energy is minimum (d) Potential energy is maximum | 11 |

756 | A car travelling at ( 60 k m / h ) overtakes another car travelling at ( 42 k m / h ) Assuming each car to be ( 5.0 m ) long, the time taken for the over taking is ( mathbf{A} cdot 6 s ) B . ( 4 s ) c. ( 3 s ) D. ( 2 s ) | 11 |

757 | A particle rotates along a circle of radius ( R=sqrt{2} mathrm{m} ) with an angular acceleration ( boldsymbol{alpha}=frac{boldsymbol{pi}}{boldsymbol{4}} boldsymbol{r} boldsymbol{a} boldsymbol{d} / boldsymbol{s}^{2} ) starting from rest. Calculate the magnitude of average velocity of the particle over the time it rotates a quarter circle. | 11 |

758 | A particle starts from the origin of coordinates at time ( t=0 ) and moves in the ( x y ) plane with a constant acceleration ( alpha ) in the ( y ) -direction. Its equation of motion is ( y=beta x^{2} ). Its velocity component in the x-direction is A. variable B. ( sqrt{frac{2 alpha}{beta}} ) c. ( frac{alpha}{beta} ) D. ( sqrt{frac{alpha}{2 beta}} ) | 11 |

759 | When the earth completes one revolution around the sun, the displacement of the earth is zero. True or false. A. True B. False | 11 |

760 | A body is projected at ( t=0 ) with a velocity ( 10 m s^{1} ) at an angle of 60 with the horizontal.The radius of curvature of its trajectory at ( t=1 s ) is ( R . ) Neglecting air resistance and taking acceleration due to gravity ( g=10 ) ms2, the value of ( boldsymbol{R} ) is : A ( .2 .4 m ) B. ( 10.3 m ) ( c .2 .8 m ) D. ( 5.1 mathrm{m} ) | 11 |

761 | Find the magnitude of the angular acceleration of the cone A ( .3 .3 mathrm{rad} / mathrm{s}^{2} ) B . ( 2.6 mathrm{rad} / mathrm{s}^{2} ) c. 2.3 rad / ( s^{2} ) D. ( 3.6 mathrm{rad} / mathrm{s}^{2} ) | 11 |

762 | A projectile is fired 30.0 degrees above the horizontal with speed ( left|boldsymbol{v}_{1}right|=mathbf{4 0 m} / boldsymbol{s} ) and a second one 60.0 degrees above the horizontal with speed ( left|boldsymbol{v}_{2}right|=mathbf{3 0 m} / boldsymbol{S} ) simultaneously. After 2 seconds, how far apart will the two projectiles be? Assume no air resistance and that they are fired from the same spot, and that each moves independent of the outer projectile. Take ( boldsymbol{g}=mathbf{9 . 8 1 m} / boldsymbol{s}^{2} ) A . ( 11.96 m ) в. ( 28.11 m ) ( mathrm{c} .39 .28 mathrm{m} ) D. 41.06 m E . ( 41.99 mathrm{m} ) | 11 |

763 | 40. The horizontal distance of the ball from the foot of the building where the ball strikes the horizontal ground will be a. V2R b. (1 + V2)R c. 2(1+12) d. 12R | 11 |

764 | U TU – 1 8. For a given velocity, a projectile has en velocity, a projectile has the same range R for two angles of projection if t, and t, are the of projection if t, and t, are the times of flight in the two cases then (a) tt, « R2 (b) 112 «R (C) 4t2« (d) 1126 | 11 |

765 | A body of mass m moving at a constant velocity v hits another body of the same mass moving with a velocity v/2 but in the opposite direction and sticks to it. The common velocity after collision is ( A ) B. v/ c. ( 2 v ) D. v/2 | 11 |

766 | (2) Explaıri clearly, wırn ex ( mathbf{S}, ) Ine distinction between: (a) magnitude of displacement over an interval of time and the total length of path covered by a particle over the same interval; (b) magnitude of average velocity over an interval of time, and the average speed over the same interval. Show in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the equality sign true? (ii) A man walks on a straight road from his home to a market ( 2.5 k m ) away with a speed of ( 5 k m h^{-1} ). Finding the market closed, he instantly turns and walks back home with a speed of ( 7.5 k m h^{-1} . ) What is the: (a) magnitude of average velocity, and (b) average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to ( mathbf{5 0 m i n},(text { iii) } 0 text { to } 40 m i n ? ) | 11 |

767 | A particle is revolving in a circle of radius ( r . ) Its displacement after completing half the revolution will be ( mathbf{A} cdot pi r ) B . ( 2 r ) c. ( 2 pi r ) D. ( frac{r}{2} ) | 11 |

768 | Find the time dependence of the velocity ( overrightarrow{boldsymbol{v}} ) vector. A ( . vec{v}=2 a vec{i}-b t vec{j} ) B . ( vec{v}=-2 a vec{i}-2 b t vec{j} ) C ( . vec{v}=-2 a vec{i}-b t vec{j} ) D. ( vec{v}=a vec{i}-2 b t vec{j} ) | 11 |

769 | A body is projected with velocity ( 24 m s^{-1} ) making an angle ( 30^{circ} ) with the horizontal. The vertical component of its velocity after ( 2 s ) is ( left(g=10 m s^{-2}right) ) A. ( 8 m s^{-1} ) upward B. ( -8 m s^{-1} ) downward c. ( 32 m s^{-1} ) upward D. ( 32 m s^{-1} ) downward | 11 |

770 | Two stones ( A ) and ( B ) are projected simultaneously from the top of a ( 100- ) ( m ) high tower. Stone B is projected horizontally with speed ( 10 m s^{-1} ). and stone ( A ) is dropped from the tower. Find out the following: (a) Time of flight of the two stone (b) Distance between two stones after 3 ( mathbf{S} ) (c) Angle of strike with ground | 11 |

771 | A particle is projected horizontally with a speed u from the top of a plane inclined at an angle ( theta ) with the horizontal. How far from the point of projection will the particle strike the plane? ( ^{mathrm{A}} cdot frac{2 u^{2}}{g} tan theta sec theta ) B. ( frac{2 u}{8} tan ^{2} theta sec theta ) c. ( frac{2 u^{2}}{g} tan theta cos theta ) D. ( frac{2 u}{g} tan theta cos ^{2} theta ) | 11 |

772 | Motion of wheel of a bicycle is (projectile, circular) motion. | 11 |

773 | Illustration 5.41 A political party has to start its procession in an area where wind is blowing at a speed of 30v2 kmh and party flags on the cars are fluttering along north-east direction. If the procession starts with a speed of 40 km h- towards north, find the direction of flags on the cars . | 11 |

774 | Is it possible to have an accelerated motion with a constant speed? Explain | 11 |

775 | 8. A body is projected up with a speed ‘u’ and the time taken by it is T to reach the maximum height H. Pick out the correct statement (a) It reaches H/2 in T/2 sec (b) It acquires velocity ul2 in T/2 sec (c) Its velocity is u/2 at H/2 (d) Same velocity at 2T | 11 |

776 | Which of the following remains constant in uniform circular motion: Speed or Velocity or both? | 11 |

777 | Fig. 3.73 21. A particle of m = 5 kg is momentarily at rest at 1=0. It is acted upon by two forces F and F. F IO • The direction and magnitude of F, are unknown. The particle experiences a constant acceleration, a , in the direction as shown in Fig. 3.74. Neglect gravity. ут t = 70 ÎN a = 10 m/s2 53° Fig. 3.74 a. Find the missing force F. b. What is the velocity vector of the particle at t = 10 s? c. What third force, F3, is required to make the acceleration of the particle zero? Either give magnitude and direction of F, or its components. | 11 |

778 | 900 29. A projectile is fired with a velocity v at right angle to the slope inclined at an angle with the horizontal. The range of the projectile along the inclined plane is 2v2 tane v² seco A Fig. A.13 a. 2v2 tan 0 sec o Eco – d. v² sino s 20 A 111 11 1 11 | 11 |

779 | A truck starts from rest and accelerates uniformly at ( 2.0 m s^{-2} . ) At ( t=10 s, ) a stone is dropped by a person standing on the top of the truck (6 ( m ) high from the ground). What are the (a) velocity, and (b) acceleration of the stone at ( t= ) 11 ( s ) ? (Neglect air resistance.) | 11 |

780 | An elevator is going up vertically with a constant acceleration of ( 2 mathrm{m} / mathrm{s}^{2} ). at the instant when its velocity is ( 4 mathrm{m} / mathrm{s} ) a ball is projected from the floor of the elevator with a speed of ( 4 mathrm{m} / mathrm{s} ) relative to the floor with an angular elevation of ( 30^{circ} . ) the time taken by te ball to return to the floor is : (take ( g=10 m / s^{2} ) ) A ( cdot frac{1}{3} mathrm{sec} ) B. ( frac{1}{sqrt{3}} sec ) c. ( frac{2}{sqrt{3}} sec ) D. ( sqrt{3} mathrm{sec} ) | 11 |

781 | The velocity vector of a particle moving in the xy plane is given by ( v=t i+x j ). If initially, the particle was at origin then the equation of trajectory of the projectile is: A ( cdot 4 x^{2}-9 y=0 ) B. ( 9 x^{2}-2 y^{3}=0 ) c. ( 16 x^{3}-9 y^{2}=0 ) D. ( 9 x^{3}-2 y^{2}=0 ) | 11 |

782 | A particle stars from rest covers a distance of x with constant acceleration then move with constant velocity and cover distance ( 2 x ) then after come to rest will constant retardation with cover distance of ( 3 x, ) then ratio of ( V_{max } / V_{text {avg }} ) will be ( A cdot 3: 5 ) B. 5: 3 c. 7: D. 5: | 11 |

783 | When particles moves in a circle at a constant speed then the motion is said to be A. Uniform motion B. Non uniform motion c. Projectile motion D. All | 11 |

784 | 5. A ball is projected from the Fig. A.44 origin. The r- and y-coordinates of its displacement are given by x = 3t and y = 41 – 51. Find the velocity of projection (in ms). maximum distances while Al | 11 |

785 | A body moving along a circular path may have A. A constant speed B. A constant velocity c. No tangential velocity D. No radial acceleration | 11 |

786 | U. Slalomuus (1) un ain appears 19. Rain appears to fall vertically to a man walking at 3 km but when he changes his speed to double, the rain app to fall at 45° with vertical. Study the following stater and find which of them are correct. i. Velocity of rain is 213 km – . The angle of fall of rain (with vertical) i O= tan – iii. The angle of fall of rain (with vertical) je 8 = sin iv. Velocity of rain is 312 kmh ! a. Statements (i) and (ii) are correct. b. Statements (i) and (iii) are correct. c. Statements (iii) and (iv) are correct. d. Statements (ii) and (iv) are correct. : 200 | 11 |

787 | Let ( vec{F} ) be the force acting on a particle having position vector ( vec{r} ) and ( vec{tau} ) be the torque of this force about the origin then: ( mathbf{A} cdot vec{r} cdot vec{Gamma}=0 ) and ( vec{F} cdot vec{Gamma} neq 0 ) B . ( vec{r} . vec{Gamma} neq 0 ) and ( vec{F} . vec{Gamma}=0 ) c. ( vec{r} . vec{Gamma} neq 0 ) and ( vec{F} cdot vec{Gamma} neq 0 ) D. ( vec{r} . vec{Gamma}=0 ) and ( vec{F} cdot vec{Gamma}=0 ) | 11 |

788 | ( (overline{mathbf{A}}+overline{mathbf{B}}) times(overline{mathbf{A}}-overline{mathbf{B}}) ) is: A ( cdotleft(bar{A}^{2}-bar{B}^{2}right) ) в. ( 2 overline{mathrm{AB}} ) c. ( 2(overline{mathrm{A}} times overline{mathrm{B}}) ) D. ( 2(overline{mathrm{B}} times overline{mathrm{A}}) ) | 11 |

789 | Two balls are projected making an angle of 30 and 45 respectively with the horizontal. If both have the same velocity at the highest points of their paths, then the ratio of their velocities of projection is A. ( sqrt{3}: sqrt{2} ) B. ( sqrt{2}: 1 ) c. ( sqrt{2}: sqrt{3} ) D. ( sqrt{3}: 2 ) | 11 |

790 | Show that ( mathbf{a} .(mathbf{b} times mathbf{c}) ) is equal in magnitude to the volume of the parallelopiped formed on the three vectors, a, b and c. | 11 |

791 | I nree points are located at the vertıces of an equilateral triangle having each side as ( alpha . ) All the points move simultaneously with speed ( u ) such that first point continually heads for second, the second for the third and the third for the first. Time taken by the points to meet at the centre is A ( cdot frac{alpha}{3 u} ) B. ( frac{2 alpha}{3 u} ) c. ( frac{alpha^{2}}{u^{3}} ) ( D cdot 3 alpha ) ( 2 u ) | 11 |

792 | 100 m 100 m 16. Three boys are running on a equitriangular track with the same speed 5 ms. At start, they were at the three corners with velocity along indicated directions. The velocity of BAO 100 m approach of any one of them towards Fig. A.9 another at t = 10 s equals a. 7.5 ms-1 b. 10 ms-c. 5 ms-1 d. Oms-1 60°C | 11 |

793 | What is the centripetal acceleration of the ball if its mass is doubled? ( A cdot a / 4 ) B. a/2 ( c ) D. 2a E. ( 4 a ) | 11 |

794 | If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is: ( mathbf{A} cdot 0^{circ} ) B. ( 90^{circ} ) ( c cdot 45^{circ} ) D. ( 180^{circ} ) | 11 |

795 | Fig. A.31 14. The distance of the point from point lands is a. 80 m b. 100 m c. 200 m where the package d. 160 m | 11 |

796 | It takes you 9.5 minutes to walk with an average velocity of ( 1.2 m / s ) to the north from the bus stop to museum entrance. What is your displacement? (in m) A. 684 в. 540 c. 525 D. 565 | 11 |

797 | A ball is thrown horizontally from a point ( 100 mathrm{m} ) above the ground with a speed of ( 200 mathrm{m} / mathrm{s} ). Find (a) the time it takes to reach the ground, (b) the horizontal distance it travels before reaching the ground, (c) the velocity (direction and magnitude) with which it strikes the ground. | 11 |

798 | 30. A grasshopper can jump a maximum distance 1.6 m. It spends negligible time on the ground. How far can it go in 10 s? a. 52 m b. 102 m c. 2012 m d. 40 V2 m | 11 |

799 | Illustration 3.9 A force of 15 N acts on a box as shown in Fig. 3.25. What are the horizontal component and vertical components of the force? 15 N Vertical component 60° Horizontal component Fig. 3.25 | 11 |

800 | Find the unit vector in the direction of sum of the vectors (1,1,1),(2,-1,-1) and ( (mathbf{0}, mathbf{2}, mathbf{6}) ) | 11 |

801 | simultaneously from point A. P moves along a smooth horizontal wire ( A B . Q ) moves along a curved smooth track. ( Q ) has sufficient velocity at ( A ) to reach ( B ) always remaining in contact with the curved track. At A, the horizontal component of velocity of ( Q ) is same as the velocity of ( mathrm{P} ) along the wire. The plane of motion is vertical. If ( t_{1}, t_{2}, ) are times taken by ( P & Q ) respectively to reach B then (Assume velocity of P is constant) ( mathbf{A} cdot t_{1}=t_{2} ) ( mathbf{B} cdot t_{1}>t_{2} ) ( mathbf{c} cdot t_{1}<t_{2} ) D. none of these | 11 |

802 | A river flows ( 3 mathrm{km} / mathrm{h} ) and a man is capable of swimming at the rate of ( 2 k m / h . ) He wishes to cross it such that the displacement parallel to river is minimum. In which direction should he swim? ( ^{A} cdot sin ^{-1}left(frac{2}{3}right) ) B. ( cos ^{-1}left(frac{2}{3}right) ) ( ^{mathbf{c}} cdot tan ^{-1}left(frac{2}{3}right) ) D. ( cot ^{-1}left(frac{2}{3}right) ) | 11 |

803 | 6. A stone projected with a velocity u at an angle with the horizontal reaches maximum height H. When it is projected with velocity u at an angle( -e with the horizontal, it reaches maximum height H,. The relation between the horizontal range R of the projectile H, and H is (a) R=4/H,H, (b) R = 4(H, -H) H2 (c) R = 4(H, +H) (d) R=HT HŽ | 11 |

804 | (1):In uniform circular motion, tangential acceleration is zero. (2) : In uniform circular motion, velocity is constant. A. Both 1 and 2 are true and 2 is correct explanation of B. Both 1 and 2 are true and 2 is not correct explanation of 1 c. 1 is true and 2 is false D. 1 is false and 2 is true | 11 |

805 | A vehicle starts from rest and moves at uniform acceleration such that its velocity increases by ( 3 m s^{-1} ) per every second. If diameter of wheel of that vehicle is ( 60 mathrm{cm}, ) the angular acceleration of wheel is: A .5 rads( ^{-2} ) B. 10 rads( ^{-2} ) C .15 rads( ^{-2} ) D. 20 rads ( ^{-2} ) | 11 |

806 | A particle moves in the ( x ) -y plane with the velocity ( overrightarrow{boldsymbol{v}}=boldsymbol{a} hat{boldsymbol{i}}+boldsymbol{b} boldsymbol{t} hat{j} . ) AT the instant ( mathrm{t}=a sqrt{3} / b ) the magnitude of tangential normal and total acceleration are | 11 |

807 | An aeroplane pilot wishes to fly due west. A wind of ( 100 mathrm{km} h^{-1} ) is blowing towards south. a. If the speed of the plane (its speed in still air) is ( 300 mathrm{km} h^{-1}, ) in which direction should the pilot head? What is the speed of the plane with respect to ground? IIlustrate with a vector diagram. | 11 |

808 | A pendulum bob of mass ( m=80 m g ) carrying a charge of ( boldsymbol{q}=boldsymbol{2} times mathbf{1 0}^{-8} boldsymbol{C} ), is at rest a horizontal uniform electric field of ( boldsymbol{E}=mathbf{2 0}, mathbf{0 0 0} boldsymbol{V} / boldsymbol{m} . ) The tension ( boldsymbol{T} ) in the thread of the pendulum and the angle ( alpha ) it makes with vertical is (take ( boldsymbol{g}=mathbf{9} . boldsymbol{8} boldsymbol{m} / boldsymbol{s}^{2} boldsymbol{)} ) This question has multiple correct options A ( cdot alpha approx 27^{circ} ) в. ( T approx 880 mu N ) c. ( T=8.8 mu N ) D. ( alpha approx 356 o ) | 11 |

809 | 10. A body is projected with velocity u at an angle of projection with the horizontal. The direction of velocity of the body makes angle 30° with the horizontal at t=2s and then after 1 s it reaches the maximum height. Then a. u= 20/3 ms, b. 0 = 60° c. = 30° d. u=1073 ms- | 11 |

810 | 8. A police jeep is chasing a culprit going on a motorbike The motorbike crosses a turning at a speed of 72 kmh! The jeep follows it at a speed of 90 kmh-, crossing the turning 10 s later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike? (In km) | 11 |

811 | A man crosses a ( 320 mathrm{m} ) wide river perpendicular to the current in 4 min. If in still water he can swim with a speed ( 5 / 3 ) times that of the current, then the speed of the current, in ( m ) min( ^{-1} ) is? A . 30 B . 40 c. 50 D. 60 | 11 |

812 | A particle is projected horizontally from the top of a tower with a velocity ( v_{0} . ) If ( v ) be its velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to ( mathbf{A} cdot v^{3} ) B ( cdot v^{2} ) c. D. ( frac{1}{v} ) | 11 |

813 | Distinguish clearly between distance and displacement of a projectile. | 11 |

814 | If we hang a body of mass ( m ) with the cord, the tension can be given as: | 11 |

815 | 9. Consider a disc rotating in the horizontal plane with a constant angular speed o about its center 0. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in Fig. A.54. When the disc is in the orientation as shown, two pebbles Pand Q are simultaneously projected at an angle towards R. The velocity of projection in the y-z plane and is same for both pebbles with respect to the disc. Assume that (1) they land back on the disc before the disc has completed 1/8 rotation, (ii) their range is less than half the disc radius, and (iii) o remains constant throughout. Then Fig. A.54 (IIT JEE, 2012) a. P lands in the shaded region and Q in the unshaded region. b. P lands in the unshaded region and Q in the shaded region. c. Both P and land in the unshaded region. d. Both P and Q land in the shaded region. | 11 |

816 | c. a = d2 61. If block A is moving horizontally with velocity find the velocity of block B at the instant as Fig. 6.341. locity then as shown Fig. 6.341 HVA XVA 2√x² +h² UVA hva 24x²+h² x² +h² | 11 |

817 | A particle is moving around a circular path with uniform angular speed ( ( omega ) ). The radius of the circular path is ( (r) ) The acceleration of the particle is A. ( frac{omega^{2}}{r} ) в. ( frac{omega}{r} ) ( c . v_{w} ) D. ( v r ) | 11 |

818 | Prove that the distance s metres, which a body falling from rest covers in time seconds is 4.9 times the square of the time t. | 11 |

819 | A body falling freely from rest covers ( frac{7}{16} ) of the total height in the last second of its fall. What is the height from which it falls? ( mathbf{A} cdot 24.2 m ) в. ( 40 m ) c. ( 80 m ) D. ( 46.8 m ) | 11 |

820 | A particle moves on the curve ( y=frac{x^{4}}{4} ) where ( boldsymbol{x}=boldsymbol{t} / 2, mathbf{x} ) and ( mathbf{y} ) are measured in metre and ( t ) in second. At ( t=4 s, ) find the velocity of particle. | 11 |

821 | A boy is running along the circumference of a stadium with constant speed. Which of the following is changing in this case? A. Centripetal force acting on the boy B. Distance covered per unit time c. Direction in which the boy is running D. Magnitude of acceleration | 11 |

822 | Figure ( (3-E 6) ) shows ( x-t ) graph of a particle. Find the time ( t ) such that the average velocity of the particle during the period 0 to ( t ) is zero | 11 |

823 | 53. A body is projected up along a smooth inclined plane with velocity u from the point A as shown in Fig. 5.199. The angle of inclination is 45°Ã 40 m and the top is connected to a well of diameter 40 m. If the body just Fig. 5.199 manages to cross the well, what is the value of u? The length of inclined plane is 2012 m. a. 40 ms -1 b. 40/2 ms -1 c. 20 ms-1 d. 20/2 ms -1 | 11 |

824 | The rate of change of displacement with time is A. Speedd B. Acceleration c. Retardation D. Velocity | 11 |

825 | 23. A ship A streams due north at 16 kmh- and a ship B due west at 12 kmh . At a certain instant B is 10 km north east of A. Find the a. magnitude of velocity of A relative to B. b. nearest distance of approach of ships. | 11 |

826 | A man is going in a topless car with a velocity of ( 10.8 k m / h . ) It is raining vertically downwards. He has to hold the umbrella at an angle of ( 53^{circ} ) to the vertical to protect himself from rain. The actual speed of the rain is ( left(cos 53^{circ}=right. ) ( left.frac{3}{5}right) ) A ( .2 .25 mathrm{ms}^{-1} ) B. ( 3.75 mathrm{ms}^{-1} ) c. ( 0.75 mathrm{ms}^{-1} ) D. ( 2.75 mathrm{ms}^{-1} ) | 11 |

827 | u. Nesuitaill verOCITY UI Dual Is JV 2. A stationary person observes that rain is falling down at 30 kmh . A cyclist is moving up on an mo plane making an angle 30° with horizontal at 10 kmh . In which direction should the cyclist hold his umorena prevent himself from the rain? 3) a. At an angle tan with inclined plane b. At an angle tan with horizontal c. At an angle tam ” ( 19 ) with inclined plane C. At an angle tan with inclined plane d. At an angle tan with vertical | 11 |

828 | A object starts from rest at ( t=0 ) and accelerates at a rate given by ( a=6 t ) What is its velocity? A ( .6 t ) B. ( 3 t^{2} ) ( c cdot 6 t^{2} ) D. 0 | 11 |

829 | 1. A body of mass m is thrown upwards at an angle with the horizontal with velocity v. While rising up the velocity of the mass after 1 seconds will be (a) V(v cos 0)2 + (v sin o)? (b) Viv cos 0 – v sin 0)2 – gt (e) Vo?+ g?-(2v sin O) g (d) Vu2+g2 – (2v cos 6) gt | 11 |

830 | When particle revolves with uniform speed on a circular path A. no force acts on it B. no acceleration acts on it it c. no work is done by it D. its velocity is constant | 11 |

831 | 9. If the resultant of n forces of different magnitudes acting at a point is zero, then the minimum value of n is (a) 1 (6) 2 (c) 3 (d) 4 | 11 |

832 | -U13 U12 U15 C2015 . 09. The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y=(8t – 50) m and x = 6t m, where t is in seconds. The velocity with which the projectile | 11 |

833 | 30. A ball rolls off the top of a stairway with a horizontal velocity of magnitude 1.8 ms. The steps are 0.20 m high and 0.20 m wide. Which step will the ball hit first (8 = 10 ms?) 30 | 11 |

834 | The free end of a thread wound on a bobbin is passed round a nail ( boldsymbol{A} ) hammered into the wall. The thread is pulled at a constant velocity. Assuming pure rolling of bobbin, find the velocity ( v_{0} ) of a center of theybobbin at heh center at he instant when the thread forms an angle ( alpha ) with the vertical. A ( cdot frac{v R}{R sin alpha-r} ) в. ( frac{v R}{text { R } sin alpha+r} ) c. ( frac{2 v R}{text { Rsind }+r} ) D. ( frac{v}{text { Rsin } alpha+r} ) | 11 |

835 | 8. The displacement of ball w.r.t. ground during its flight is a. 32.64 m b. 2 m c. 52 m d. 30.64 m | 11 |

836 | The velocity ( v ) of waves produced in water depends on their wavelength ( lambda ) the density of water ( rho, ) and acceleration due gravity ( g ). The square of velocity is proportional to: ( mathbf{A} cdot K sqrt{(g lambda)} ) B . ( lambda^{-1} g^{-1} rho^{-1} ) c. ( lambda rho g ) D. ( lambda^{2} g^{-2} rho^{-1} ) | 11 |

837 | Illustration 5.61 Two particles A and B are moving with constant velocities v, and v2. At t = 0, v, makes an angle e, with the line joining A and B and v, makes an angle e, with the line joining A and B. Find their velocity of approach. VI 02 Fig. 5.126 | 11 |

838 | In a Rutherford scattering experiment when a projectile of charge ( Z_{1} ) and mass ( M_{1} ) approaches a target nucleus of charge ( Z_{2} ) and mass ( M_{2} ) the distance to closest approached is ( r_{0} . ) The energy of the projectile is A . directly proportional to ( M_{1} times M_{2} ) B. directly proportional to ( Z_{1} Z_{2} ) C. directly proportional to to ( Z_{1} ) D. directly proportional to mass ( M_{1} ) | 11 |

839 | Which of the following is the unit vector perpendicular to ( vec{A} ) and ( vec{B} ) ? ( A cdot frac{widehat{A} times widehat{B}}{A B sin theta} ) B. ( frac{widehat{A} times widehat{B}}{A B cos theta} ) c. ( frac{vec{A} times vec{B}}{A B sin theta} ) D. ( frac{vec{A} times vec{B}}{A B cos theta} ) | 11 |

840 | 34. Which of the following pairs of forces cannot be added to give a resultant force of 4 N? a. 2 N and 8N b. 2 N and 2 N c. 2 N and 6N d. 2 N and 4 N | 11 |

841 | Uniform circular motion is called continuously accelerated motion mainly because its : A. direction of motion changes B. speed remains the same c. velocity remains the same D. direction of motion does not change | 11 |

842 | The shortest possible time required by the boat to cross the river will be:- A. 125 sec B. 250 sec C . 500 sec D. ( frac{250}{sqrt{3}} ) sec | 11 |

843 | If air resistance is not considered in projectiles, the horizontal motion takes place with : A. Constant velocity B. Constant acceleration c. constant retardation D. Variable velocity | 11 |

844 | 6. The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. The angle between A and B is (a) 120° (b) 150° (c) 135° (d) None of these | 11 |

845 | On a linear escalator running between two points ( A ) and ( B, ) a boy takes time ( t_{1} ) to move from ( A ) to ( B ), if the boy runs with a constant speed on the escalator. If the boy runs from ( B ) to ( A ), he takes time ( t_{2} ) to reach ( B ) from ( A ). The time taken by the boy to move from ( boldsymbol{A} ) to ( boldsymbol{B} ) if he stands still on the escalator will be (The escalator moves from ( boldsymbol{A} ) to ( boldsymbol{B} ) ) A ( cdot frac{t_{1} t_{2}}{t_{2}-t_{1}} ) В. ( frac{2 t_{1} t_{2}}{t_{2}-t_{1}} ) c. ( frac{t_{1}^{2}+t_{2}^{2}}{t_{1} t_{2}} ) D. ( frac{t_{1}^{2}-t_{2}^{2}}{t_{1} t_{2}} ) | 11 |

846 | For two particular vectors ( vec{A} ) and ( vec{B} ) it is known that ( overrightarrow{boldsymbol{A}} times overrightarrow{boldsymbol{B}}=overrightarrow{boldsymbol{B}} times overrightarrow{boldsymbol{A}} . ) What must be true about the two vectors? A. At least one of the two vectors must be the zero vector в. ( vec{A} times vec{B}=vec{B} times vec{A} ) is true for any two vectors c. one of the two vectors is a scalar multiple of the other vector. D. The two vectors must be perpendicular to each other | 11 |

847 | If ( A B C D ) is a parallelogram, ( A B= ) ( mathbf{2} hat{mathbf{i}}+mathbf{4} hat{mathbf{j}}-mathbf{5} hat{boldsymbol{k}} ) and ( boldsymbol{A} boldsymbol{D}=hat{boldsymbol{i}}+mathbf{2} hat{boldsymbol{j}}+mathbf{3} hat{boldsymbol{k}} ) then the unit vectors in the direction of ( B D ) is A ( cdot frac{1}{sqrt{69}}(hat{i}+2 hat{j}-8 hat{k}) ) B ( cdot frac{1}{69}(hat{i}+2 hat{j}-8 hat{k}) ) c. ( frac{1}{sqrt{69}}(-hat{i}-2 hat{j}+8 hat{k}) ) D ( cdot frac{1}{69}(-hat{i}-2 hat{j}+8 hat{k}) ) | 11 |

848 | Position vector that defines position of vector in three dimensions having formula of A ( cdot sqrt{left(a^{2}+b^{2}+c^{2}right)} ) B. ( sqrt{(a+b+c)} ) C ( cdot sqrt{left(a^{2}-b^{2}+c^{2}right)} ) D. ( left(a^{2}+b^{2}+c^{2}right) ) | 11 |

849 | A person observes that rain strikes him normally when he is moving with 2 kmph. When he reverses his direction and moves with the same speed, the rain will strike him at an angle ( 45^{circ} ) with the vertical. Determine the true velocity of rainfall is? A ( cdot 2 sqrt{5} ) kmph B. ( sqrt{2} ) kmph c. ( 5 sqrt{2} ) kmph D. ( sqrt{5} ) kmph | 11 |

850 | 29. A stone is projected from the point on the ground in sa a direction so as to hit a bird on the top of a telegraph po of height h and then attain the maximum height 3h/2 above the ground. If at the instant of projection the bird were to fly away horizontally with uniform speed, find the ratio between horizontal velocities of the bird and stone if the stone still hits the bird while descending. | 11 |

851 | A rotating wheel has a speed of 1200 rpm and the it is made to slow down at a constant rate at 2 rad( / s^{2} ). The number of revolution it makes before coming to rest will be: | 11 |

852 | A golfer swings a golf club so that the end of the club is moving ( 30 mathrm{m} / mathrm{s} ) when it strikes the ball. The radius of the circular path for the end of the club (which includes the club and the golfer’s arms ) is ( 1.8 mathrm{m} ) What is the centripetal acceleration of the end of the club as it strikes the ball? ( mathbf{A} cdot 500 m / s^{2} ) B. ( 1.7 mathrm{m} / mathrm{s}^{2} ) ( mathbf{c} cdot 0.06 m / s^{2} ) D. ( 54 mathrm{m} / mathrm{s}^{2} ) E . ( 0 mathrm{m} / mathrm{s}^{2} ) | 11 |

853 | . 21 a. 1 1 10. An object is moving in the x-y plane with the position as a function of time given by i = x(t)i + y(t)j. Point O is at x = 0, y = 0. The object is definitely moving towards O when a. V > 0,, > 0 b. Vx < 0,vy < 0 c. xvx + yv, 0 | 11 |

854 | = 16. The relative velocity of B as seen from A in a. -8√2 + 6/2 b. 4√2 + 3/3) c. 3/5i + 2√3 d. 3/27 +4√37 e | 11 |

855 | When a body moves along a circular path,its direction of speed A. remains constant B. keep changing continuosly c. may change sometime D. cant be predicted | 11 |

856 | The rear wheels of a car are turning at an angular speed of 60 rad/s. The brakes are applied for 5 s, causing a uniform angular retardation of ( 8 r a d / s^{-2} . ) The number of revolutions turned by the rear wheels during the braking period is about: A . 48 B. 96 ( c .32 ) D. 12 | 11 |

857 | The distance PQ is? ( mathbf{A} cdot 20 mathrm{m} ) ( mathbf{B} cdot 10 sqrt{3} mathrm{m} ) ( c cdot 10 m ) D. 5 m | 11 |

858 | In uniform circular motion, the factor that remains constant is : A. acceleration B. momentum c. kinetic energy D. linear velocity | 11 |

859 | ( |overline{mathbf{a}} cdot overline{mathbf{b}}|^{2}-|overline{mathbf{a}} times overline{mathbf{b}}|^{2}= ) ( mathbf{A} cdot a b cos theta ) B ( cdot a^{2} b^{2} cos theta ) C ( cdot a^{2} b^{2} cos 2 theta ) ( mathbf{D} cdot a b cos 2 theta ) | 11 |

860 | The position of a particle moving in the ( X ) -Y plane from origin at any time ( t ) is given by ( boldsymbol{x}=left(mathbf{3} boldsymbol{t}^{2}-mathbf{6} boldsymbol{t}right) mathbf{m} ; boldsymbol{y}=left(boldsymbol{t}^{2}-right. ) ( 2 t) mathrm{m}, ) where ( t ) is in seconds. Select the correct statement(s) about the moving particle from the following. A. The acceleration of the particle is zero at ( t=0 ) second B. The velocity of the particle is zero at ( t=0 ) second c. The velocity of the particle is zero at ( t=1 ) second D. The velocity and acceleration of the particle are never zero | 11 |

861 | 33. The projection speed is : a. 137 ms c. 114 ms -1 b. 141 ms-1 d. 140 ms-1 | 11 |

862 | 3. The range R of projectile is same when its maximum heights are h, and hy. What is the relation between R, hj, and h? a. R=sh b. R= √2hh c. R=2 sm d. R=4 /hh | 11 |

863 | 21. The vertical height h of P from 0, a. 10 m b . 5 m c. 15 m d. 20 m um boicotettoia L.. .1. C. | 11 |

864 | DULU. MULTI 26. Find the magnitude of the unknown forces 11 all forces is zero Fig. 3.75. 15 539 90° 10 Fig. 3.75 | 11 |

865 | turp lali A boy on a train of height h, projects a coin to his friend of height h, standing on the same train, with a velocity v relative to the train, at an angle with horizontal. If the train moves with a constant velocity V’ in the direction of x-motion of the coin, find the (a) distance between the boys so that the second boy can catch the coin, (b) maximum height attained by the coin, and (c) speed with which the second boy catches the coin relative to himself (train) and ground | 11 |

866 | A bead of mass ( m ) slides on a hemispherical surface with a velocity ( boldsymbol{v} ) at an angular position ( theta ). If the coefficient of friction between the bead and hemispherical surface is ( mu, ) Find the magnitude of Angular momentum of the bead about ( O ) in the position shown. | 11 |

867 | A trian of length ( 200 m ), travelling at ( 30 m s^{-1} ) overtakes another train of length ( 300 m ) travelling at ( 20 m s^{-1} . ) The time taken by the first train to pass the second train is A .30 sec B. 50 sec c. 10 sec D. 40 sec | 11 |

868 | L. 48WS 5. The correct velocity-time graph for the rocketeer would be a. VA b. 1 d. vf | 11 |

869 | A small object of mass ( m, ) on the end of a light cord, is held horizontally at a distance ( r ) from a fixed support as shown. The object is then released. What is the tension in the cord when the object is at the lowest point of its swing? A. ( m g / 2 ) в. ( m g ) ( mathbf{c} cdot 2 m g ) D. ( 3 m g ) | 11 |

870 | At the height ( 80 m, ) an aeroplane is moving with ( 150 m / s . ) A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped? ( (text { Given } g= ) ( left.10 m / s^{2}right) ) A. ( 605.3 mathrm{m} ) B. ( 600 m ) ( c .80 m ) D. 230 ( m ) | 11 |

871 | A projectile is given an initial velocity of ( hat{mathbf{i}}+2 hat{j} . ) The cartesian equation of its path is ( left(boldsymbol{g}=mathbf{1 0} boldsymbol{m} boldsymbol{s}^{-2}right) ) A ( cdot y=2 x-5 x^{2} ) В . ( y=x-5 x^{2} ) C ( .4 y=2 x-5 x^{2} ) D. ( y=2 x-25 x^{2} ) | 11 |

872 | Find the moments of time when the particle is at the distance ( 10.0 mathrm{cm} ) from the origin. A. ( 1.1,9, ) and ( 11 s ) B. ( 1,10, ) and ( 11 s ) c. ( 1.1,10, ) and ( 11 s ) D. ( 1.1,9, ) and ( 13 s ) | 11 |

873 | What is banking of roads? Why banking is necessary for a curved road? | 11 |

874 | 7. A scooter going due east at 10 ms-1 turns right through an angle of 90°. If the speed of the scooter remains unchanged in taking turn, the change is the velocity of the scooter is (a) 20.0 ms-1 south eastern direction (b) Zero (c) 10.0 ms- in southern direction (d) 14.14 ms-l in south-west direction | 11 |

875 | A stone is moved in a horizontal circle of radius ( 4 mathrm{m} ) by means of a string at a height of ( 20 mathrm{m} ) above the ground. The string breaks and the particle’ flies off horizontally, striking the ground 10m away. The centripetal acceleration during circular motion is A ( cdot 6.25 m s^{-2} ) B. ( 12.5 m s^{-2} ) c. ( 18.75 mathrm{ms}^{-2} ) D. ( 25 m s^{-2} ) | 11 |

876 | The distances covered by a particle thrown in a vertical plane, in horizontal and vertical directions at any instant of time ‘t’ are ( x=3 t ) and ( y=4 t-5 t^{2} ) .The acceleration due to gravity is A ( .8 m / s^{2} ) B . ( 9 m / s^{2} ) ( mathrm{c} cdot 10 mathrm{m} / mathrm{s}^{2} ) D. ( 16 m / s^{2} ) | 11 |

877 | The velocity and acceleration vectors of a particle undergoing circular motion ( operatorname{are} overrightarrow{boldsymbol{v}}=2 hat{boldsymbol{i}} boldsymbol{m} / boldsymbol{s} ) and ( overrightarrow{boldsymbol{a}}=boldsymbol{2} hat{boldsymbol{i}}+ ) ( 4 hat{j} m / s^{2} ) respectively at an instant of time. The radius of the circle is A . ( 1 m ) B. ( 2 m ) ( c .3 m ) D. ( 4 m ) | 11 |

878 | 22. The maximum height attained by the particle (from the line O) a. 20.5 m b. 5 m c. 16.25 m d. 11.25 m | 11 |

879 | Why is the motion of a body moving with a constant speed around a circular path said to be accelerated? | 11 |

880 | A particle moves according to the equation ( t=sqrt{x}+3 . ) When the particle comes to rest for the first time? A . ( 3 s ) в. 2.5 ( s ) ( mathrm{c} .3 .5 mathrm{s} ) D. None of these | 11 |

881 | A ball thrown with a velocity of ( 49 m s^{-1} ) got the maximum range recorded in the atmosphere as ( 225 m ). The decrease in range due to the atmosphere is A. ( 0 m ) B. ( 245 m ) ( mathbf{c} .225 m ) D. 20m | 11 |

882 | 1. Tivo particles were projected one by one with the same initial velocity from the same point on level ground. They follow the same parabolic trajectory and are found to be in the same horizontal level, separated by a distance of 1 m. 2 s after the second particle was projected. Assume that the horizontal component of their velocities is 0.5 ms! Find a. the horizontal range of the parabolic path. b. the maximum height for the parabolic path. | 11 |

883 | An object moving with a speed of 6.25 ( mathrm{m} / mathrm{s}, ) is decelerated at a rate given by ( frac{d v}{d t}=-2.5 sqrt{v} ) where ( v ) is the instantaneous speed. The time taken by the object, to come to rest, would be then ( mathbf{A} cdot 2 s ) B . ( 4 s ) c. ( 8 s ) D. ( 1 s ) | 11 |

884 | 26. A ball thrown by one player reaches the other in 2 s. The maximum height attained by the ball above the point of projection will be about a. 2.5 m b. 5 m c . 7.5 m d. 10 m 1. T If the ti | 11 |

885 | 37. The equation of motion of a projectile is y=1 The horizontal component of velocity is 3 ms. What is the range of the projectile? a. 18 m b . 16 m c. 12 m d . 21.6 m ubon its maximum . .1 . | 11 |

886 | Two trains are each 50 m long moving parallel towards each other at speeds ( 10 m / s ) and ( 15 m / s ) respectively, at what time will they pass each other? | 11 |

887 | The components of a vector along the ( x ) and ( y ) -directions are ( (n+1) ) and 1 respectively. If the coordinate system is rotated by an angle ( theta=60^{circ} ), then the components change to ( n ) and ( 3 . ) The value of ( n ) is A .2 B. ( 1+sqrt{3} ) ( c cdot 1-sqrt{3} ) D. ( 1 pm sqrt{3} ) | 11 |

888 | A train at rest has a length of ( 100 mathrm{m} . ) At what speed must it approach a tunnel of length ( 80 mathrm{m} ) so that an observer at rest with respect to the tunnel will see that the entire train is in the tunnel at one time? A . 1.25c B. 0.8ç c. ( 0.64 c ) D. 0.6c E . ( 0.36 c ) | 11 |

889 | A curved road of ( 50 m ) in radius is banked to correct angle for a given speed. If the speed is to be doubled keeping the same banking angle, the radius of curvature of the road should be changed to A. 200 ( mathrm{m} ) B. 100 ( m ) ( c cdot 50 m ) D. None of the above | 11 |

890 | The horizontal ranges described by two projectiles, projected at angles ( left(45^{circ}-right. ) ( theta ) ) and ( left(45^{circ}+thetaright) ) from the same point and same velocity are in the ratio. A . 2: 1 B. 1: 1 ( c cdot 2: 3 ) D. 1: 2 | 11 |

891 | The resultant of two forces ( P ) and ( Q ) is ( R ) If ( Q ) is doubled and when ( Q ) is reversed ( R ) is again doubled. Show that ( P: Q: ) ( boldsymbol{R}=sqrt{mathbf{2}}: sqrt{mathbf{3}}: sqrt{mathbf{2}} ) | 11 |

892 | The sum and difference of two perpendicular vectors of equal length are A. Perpendicular to each other and of equal length B. Perpendicular to each other and of different lengths c. of equal length and have an obtuse angle between them D. of equal length and have an acute angle between them | 11 |

893 | Six persons are situated at the corners of a hexagon of side ( l ). They move at a constant speed ( v . ) Each person maintains a direction towards the person at the next corner. When will the persons meet? A. в. ( frac{2 l}{3 v} ) c. ( frac{3 l}{2 v} ) D. ( frac{2 l}{v} ) | 11 |

894 | d. 25 b. 3. c. ls d . 2. 5 38. Two balls are projected from points A and B BRO in vertical plane as shown in Fig. A.17. AB is a straight vertical line. The balls can collide in mid air if vi/v2 is equal to sine, sin 02 b. – sine, Fig. A.17 cos, coso cos O2 cos portiole in throunot met with Aloi a. sin 02 | 11 |

895 | 5 nakes an angle 20. At the point where the particle’s velocity makes an 0/2 with the horizontal e u² cos²0 sec u² cos² O sec ² 0 – a. b. 2u? cos? O sec C. u? cos? A sec30 138 | 11 |

896 | A moves with constant velocity u along then ( x ) -axis. ( B ) always has velocity towards A. After how much time will B meet ( A ) if ( B ) moves with constant speed V? What distance will be travelled by A and B? | 11 |

897 | Illustration 5.21 A boy of height 1.5 m, making move a skateboard due east with velocity 4 m s’, throws a com vertically up with a velocity of 3 ms relative to himself a. Find the total displacement of the coin relative to grown till it comes to the hand of the boy. b. What is the maximum height attained by the coin wrt ground? CUL m an from hav Aletenih | 11 |

898 | A car A moves with velocity ( 15 m s^{-1} ) and B with velocity ( 20 m s^{-1} ) are moving in opposite directions as shown in the figure. Find the relative velocity of B w.r.t. ( A ) and ( A ) w.r.t. ( B ). | 11 |

899 | A small body is thrown at an angle to the horizontal with the initial velocity ( vec{v}_{0} ) Neglecting the air drag, find the mean velocity vector ( langlevec{v}rangle ) averaged over the first ( t ) sec and over the total time of motion. A ( cdot(vec{v})_{t}=vec{v}_{0}-frac{g t}{2},langlevec{v}rangle=vec{v}_{0}-g frac{left(vec{v}_{0} gright)}{g^{2}} ) B ( cdot(vec{v})_{t}=vec{v}_{0}-frac{g t}{2},langlevec{v}rangle=vec{v}_{0}+g frac{left(vec{v}_{0} gright)}{g^{2}} ) c. ( (vec{v})_{t}=vec{v}_{0},langlevec{v}rangle=vec{v}_{0}-g frac{left(vec{v}_{0} gright)}{g^{2}} ) D. None of these | 11 |

900 | 001 ov2 39. A particle is thrown at time t = 0 with a 10 velocity of 10 ms at an angle 60° with the 13 horizontal from a point on an inclined plane, a making an angle of 30° with the horizontal. Fig. A.18 The time when the velocity of the projectile becomes parallel to the incline is 2 a. FSb. Tas C. 13 s d. Tas | 11 |

901 | Name a physical quantity that remains constant in a uniform circular motion. A. Velocity B. Acceleration c. Momentum D. Angular speed | 11 |

902 | 13. Two equal forces (P each) act at a point inclined to each other at an angle of 120°. The magnitude of their resultant is (a) P/2 (b) P/4 (c) P (d) 2P | 11 |

903 | A glass wind screen whose inclination with the vertical can be changed is mounted on a car. The car moves horizontally with a speed of ( 2 m / s . A t ) what angle ( alpha ) with the vertical should the wind screen be placed so that the rain drops falling vertically downwards with velocity ( 6 m / s ) strike the wind screen perpendicularly? ( mathbf{A} cdot tan ^{-1}(3) ) B ( cdot tan ^{-1}(4) ) c. ( tan ^{-1}left(frac{1}{3}right) ) D. ( tan ^{-1}left(frac{1}{4}right) ) | 11 |

904 | In the cube of side ‘ ( a^{prime} ) shown in the figure, the vector from the central point of the face ( A B O D ) to the central point of the face ( B E F O ) will be A ( cdot frac{1}{2} a(hat{i}-hat{k}) ) B ( cdot frac{1}{2} a(hat{j}-hat{i}) ) c. ( frac{1}{2} a(hat{k}-hat{i}) ) D. ( frac{1}{2} a(hat{j}-hat{k}) ) | 11 |

905 | A car is moving in a circular track of radius ( 10 mathrm{m} ) with a constant speed of 10 ( mathrm{m} / mathrm{s} . mathrm{A} ) plumb bob is suspended from the roof of the car by a light weight rigid rod of ( 1 mathrm{m} ) long.The angle made by the rod with track is: A. 0 B. 30 ( c cdot 45 ) D. 60 | 11 |

906 | A projectile fired from the top of a ( 40 m ) high cliff with an initial speed of ( 50 m / s ) at an unknown angle. Find its speed when it hits the ground. ( (g= ) ( left.10 m / s^{2}right) ) | 11 |

907 | If a ball is thrown vertically upwards with speed ( u, ) the distance covered during the last ( t ) seconds of its ascent is ( mathbf{A} cdot u ) в. ( frac{1}{2} g t^{2} ) c. ( u t-frac{1}{2} g t^{2} ) D. ( (u+g t) t ) | 11 |

908 | If particle takes ( t ) seconds less and acquires a velocity of ( mathrm{v} mathrm{m} / mathrm{s} ) more in falling through the same distance on to planets where the acceleration due to gravity are ( 2 g ) and ( 8 g ) respectively, then A. ( v=4 g t ) B. ( v=5 g t ) c. ( v=2 g t ) D. ( v=16 g t ) | 11 |

909 | A man can swim in still water with a velocity ( 5 mathrm{m} / mathrm{s} ). He wants to reach at directly opposite point on the other bank of a river which is flowing at a rate of ( 4 m / s . ) River is ( 15 m ) wide and the man can run with twice the velocity as compared with velocity of swimming. If he swims perpendicular to river flow and then run along the bank, then time taken by him to reach the opposite point is: A. 3 sec B. less than 3 sec c. 5 sec D. 4.2 sec | 11 |

910 | A stone is thrown vertically upward with an initial velocity ( V_{0} . ) The distance traveled in time ( 4 v_{0} / 3 g ) is ( ^{A} cdot frac{2 v_{0}^{2}}{g} ) в. ( frac{v_{0}^{2}}{2 g g g} ) ( ^{mathrm{c}} cdot frac{4 v_{0}^{2}}{9 g} ) D. ( frac{5 v_{0}^{2}}{9 g} ) | 11 |

911 | 3. The time taken to cross the river is a. h b. En czten d. none | 11 |

912 | Why is the work done on an object moving with uniform circular motion zero? | 11 |

913 | A triangular plate of uniform thickness and density is made to rotate about an axis perpendicular to the plane of the paper and (a) passing through ( boldsymbol{A} ) passing through ( B, ) by the application of some force ( boldsymbol{F} ) at ( boldsymbol{C}(operatorname{mid}- ) point of ( A B) ) as shown in fig. In which case is angular acceleration more A ( . ) in case ( (a) ) B. in case (b) c. both ( (a) ) and ( (b) ) D. none of these | 11 |

914 | A stationary man observes that the rain strikes him at an angle of ( 60^{circ} ) to the horizontal. When he begins to move with the velocity of ( 25 m / s ) then the drops appear to strike him at an angle ( 30^{circ} ) from horizontal. The velocity of the rain drops is : ( mathbf{A} cdot 25 m / s ) B. ( 50 mathrm{m} / mathrm{s} ) c. ( 12.5 m / s ) D. ( 25 sqrt{2} ) | 11 |

915 | Locating position vector of a point object | 11 |

916 | k a 28. Two particles A and B are placed A- as shown in Fig. A.12. The particle VB A, on the top of tower, is projected horizontally with a velocity u and particle B is projected along the surface Fig. A.12 towards the tower, simultaneously. If both particles meet each other, then the speed of projection of particle B is [ignore any friction] a. d) 8 b. d. V2H c. de tu d. u | 11 |

917 | If a body is projected horizontally from the top of the tower then acceleretions of the body along the vertical direction of path is A. Decreases B. Increases c. Remains same D. zero | 11 |

918 | 25. The front wind screen of a car is inclined at an angle 60° with the vertical. Hailstones fall vertically downwards with a speed of 513 ms. Find the speed of the car so that hailstones are bounced back by the screen in vertically upward direction with respect to car. Assume elastic collision of hailstones with wind screen. | 11 |

919 | Illustration 5.67 A particle moves in a circle of radius 2 cm at a speed given by v = 4t, where v is in cms and t is in seconds. a. Find the tangential acceleration at t = 1s. b. Find total acceleration at t = 1s. Sol | 11 |

920 | COMPONCINO A stone is projected from level ground with speed u an angle with horizontal. Somehow the acceleration gravity (8) becomes double (that is 2g) immediately art stone reaches the maximum height and remains same thereafter. Assume direction of acceleration due to gravity always vertically downwards. 14. The total time of flight of particle is: 3 usine (b) u sin 0(1+1) gl72) 2u sin e 2 g | 11 |

921 | Two projectiles ( A ) and ( B ) thrown with same speed but angles are ( 40^{circ} ) and ( 50^{circ} ) with the horizontal.Then A . A will fall earlier B. B will fall earlier c. both will fall at the same time D. None of these | 11 |

922 | Assertion Projectile motion is called a two dimensional motion, although it takes place in space. Reason In space it takes place in a plane. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion is incorrect but Reason is correct. | 11 |

923 | A ball is projected from the ground with a speed of ( 20 m / s ) at an angle of 45 with horizontal. There is a wall of ( 25 m ) height at a distance of ( 10 m ) from the projection point. The ball will hit the wal at a height of ( A cdot 5 m ) в. ( 7.5 m ) c. ( 10 m ) D. ( 12.5 m ) | 11 |

924 | се со цього часу 15. Two horizontal forces of magnitudes 10 N and PN act on a particle. The force of magnitude 10 N acts due west and the force of magnitude PN acts on a bearing of 30° east of north as shown in figure. The resultant of these two force acts due north. Find the magnitude of this resultant. PN 309 10 N Fig. 3.72 | 11 |

925 | If ( overrightarrow{boldsymbol{u}}=overrightarrow{boldsymbol{a}}-overrightarrow{boldsymbol{b}} ; overrightarrow{boldsymbol{v}}=overrightarrow{boldsymbol{a}}+overrightarrow{boldsymbol{b}} ) and ( |overrightarrow{boldsymbol{a}}|=|overrightarrow{boldsymbol{b}}|= ) 2 then ( |vec{u} times vec{v}| ) is equal to ( sqrt[A cdot]{2left(16-(vec{a} cdot vec{b})^{2}right)} ) в. ( 2 sqrt{left(16-(vec{a} . vec{b})^{2}right)} ) ( ^{mathrm{c}} sqrt[2]{left(4-(vec{a} cdot vec{b})^{2}right)} ) D . ( left[4-(vec{a} . vec{b})^{2}right] ) | 11 |

926 | Illustration 5.51 Rain is falling vertically and a man moving with velocity 6 ms. Find the angle at which the man should hold his umbrella to avoid getting wet. | 11 |

927 | A particle is revolving in a circle, clockwise in the plane of the circle. The angular acceleration in directed A. Towards the center in the plane of the paper. B. Radially outwards in the plane of the paper c. Perpendicular to the plane of the paper. D. Veertically in the plane of the paper. | 11 |

928 | A steamer crosses a river having a width of ( 240 m ) which is flowing with a speed of ( 8 m / s . ) In order to cross the river along the shortest path, find the time of crossing the river. [velocity of steamer in still water is ( 10 mathrm{ms}^{-1} ) ]. | 11 |

929 | 27. A ball is projected for maximum range with speed 20 ms. A boy is located at a distance 25 m from poin of throwing start run to catch the ball at the time when the ball was projected. Find the speed of the boy so that he can catch the ball (Take g = 10 ms) | 11 |

930 | A ball is projected from the ground at angle ( theta ) with the horizontal. After ( 1 s, ) it is moving at angle ( 45^{circ} ) with the horizontal and after ( 2 s ) it is moving horizontally. What is the velocity of projection of the ball? A ( cdot 10 sqrt{3} m s^{-1} ) B ( cdot 20 sqrt{3} m s^{-1} ) D. ( 20 sqrt{2} mathrm{ms}^{-1} ) | 11 |

931 | toppr Q Type your question ( r, ) as seen in the picture. If each of the diagrams among the possible answers shows flies with the same acceleration as the one pictured directly below, which fly has a speed that is twice the speed of the fly pictured directly below? ( A ) B. ( c ) radius ( =r / 2 ) D. radius ( =r / 4 ) E. None of the objects in this question are accelerating since thev al speed | 11 |

932 | Juur av uy munt un ground! 4. A platform is moving upwards with a constant acceleration of 2 ms. At time t = 0, a boy standing on the platform throws a ball upwards with a relative speed of 8 ms.At this instant, platform was at the height of 4 m from the ground and was moving with a speed of 2 ms. Take g = 10 ms. Find a. when and where the ball strikes the platform. b. the maximum height attained by the ball from the ground. c. the maximum distance of the ball from the platform. | 11 |

933 | A particle is moving in a circular path of radius r. Its displacement after moving through half the circle would be: A. zero B. ( c cdot 2 r ) D. ( frac{2}{r} ) | 11 |

934 | The angle between velocity and acceleration of a particle describing uniform circular motion is ( mathbf{A} cdot 180^{circ} ) B . ( 45^{circ} ) ( mathrm{c} cdot 90^{circ} ) D. ( 60^{circ} ) | 11 |

935 | Man A is sitting in a car moving with a speed of ( 54 mathrm{km} / mathrm{hr} ) observes a man ( mathrm{B} ) in front of the car crossing perpendicularly a road of width ( 15 mathrm{m} ) in three seconds. Then the velocity of man ( mathrm{B}(text { in } mathrm{m} / mathrm{s}) ) will be A ( .5 sqrt{10} ) towards the car at some angle B. ( 5 sqrt{10} ) away from the car at some angle c. 5 perpendicular to the road D. 15 along the road | 11 |

936 | Three forces ( vec{P}, vec{Q} ) and ( vec{R} ) acting along ( I A ) IB and IC, where I is the incentre of a ( Delta mathrm{ABC}, ) are in equilibrium. Then ( overrightarrow{mathbf{P}}: overrightarrow{mathbf{Q}}: ) ( overrightarrow{mathbf{R}} ) is: ( ^{A} cdot cos frac{A}{2}: cos frac{B}{2}: cos frac{C}{2} ) B ( cdot sin frac{mathrm{A}}{2}: sin frac{mathrm{B}}{2}: sin frac{mathrm{C}}{2} ) c. ( sec frac{mathrm{A}}{2}: sec frac{mathrm{B}}{2}: sec frac{mathrm{C}}{2} ) D ( operatorname{cosec} frac{mathrm{A}}{2}: operatorname{cosec} frac{mathrm{B}}{2}: operatorname{cosec} frac{mathrm{C}}{2} ) | 11 |

937 | 3. A boat which has a speed of 5 kmh in still water crosses a river of width 1 km along the shortest possible path in 15 min. The velocity of the river water in kmh is b. 3 c. 4 d. 141 (IIT JEE, 1988) 10. c | 11 |

938 | 35. Shots are fired simultaneously from the top and bottom of a vertical cliff with the elevation a = 30°, B = 60°, respectively (Fig. A.15). The shots strike an object AB simultaneously at the same point. If a = a = 30 3 m 30 V3 m is the horizontal distance of the Fig. A.15 object from the cliff, then the height h of the cliff is a. 30 m b. 45 m c. 60 m d. 90 m | 11 |

939 | The component of a vector r along x-axis will have maximum value if: ( A cdot r ) is along positive ( y ) -axis B. r is along positive x-axis C . r makes an angle of ( 45^{circ} ) with the x-axis D. r is along negative y-axis | 11 |

940 | A particle moves according to the equation ( boldsymbol{x}=mathbf{2} boldsymbol{t}^{2}-mathbf{5} boldsymbol{t}+boldsymbol{6} . ) The average velocity in the first ( 3 s ) and velocity at ( t=3 s ) are repectively A ( cdot 1 m s^{-1}, 7 m s^{-1} ) B. ( 4 m s^{-1}, 3 m s^{-1} ) ( mathrm{c} cdot 2 m s^{-1}, 5 m s^{-1} ) D. ( 3 m s^{-1}, 7 m s^{-1} ) | 11 |

941 | A particle located at ( x=0 ) at time ( t=0 ) starts moving along the positive ( x ) direction with a velocity ‘v’ that varies as ( boldsymbol{v}=boldsymbol{alpha} sqrt{boldsymbol{x}} . ) The displacement of the particle varies with time as? | 11 |

942 | Two trains, each ( 50 m ) long, are travelling in opposite directions with velocity ( 10 m / s ) and ( 15 m / s . ) The time of crossing is- ( mathbf{A} cdot 2 s ) B . ( 4 s ) c. ( 2 sqrt{3} s ) D. ( 4 sqrt{3} s ) | 11 |

943 | Find out the angular acceleration of a washing machine, starting from rest, accelerates within ( 3.14 s ) to a point where it is revolving at a frequency of ( mathbf{2 . 0 0 H z} ) A. ( 0.100 r a d / s^{2} ) B. ( 0.637 r a d / s^{2} ) c. 2.00 rad ( / s^{2} ) D. 4.00 rad ( / s^{2} ) E ( .6 .28 mathrm{rad} / mathrm{s}^{2} ) | 11 |

944 | Figure shows the trajectory of a projections fired at an angle ( theta ) with the horizontal. The elevation angle of the highest point as seen from the point of launching is ( varphi . ) The relation between ( varphi ) ( operatorname{ans} theta ) is A ( cdot tan phi=frac{1}{2} tan theta ) B. ( tan ^{2} phi=frac{1}{2} tan ^{2} ) ( mathbf{c} cdot sin phi=frac{1}{2} sin theta ) D. ( cos ^{2} phi=frac{1}{2} cos ^{2} theta ) | 11 |

945 | toppr Q Type your question objects moving at constant speed in circular paths are shown. The objects speeds, circular path radii, and masses are given in each diagram. In which situation does the pictured object have the greatest amount of acceleration due to its circular motion? ( A ) B. ( c ) ( D ) E. None of the object in this question is accelerating, since they all are moving at a constant speed | 11 |

946 | A particle ( P ) is fixed at certain point in horizontal plane and another particle ( Q ) is moving around ( mathrm{P} ) in circular path (with centre 0 ) of radius ‘r’ with constant speed ‘u’.’ ‘P’ observes the motion of ‘Q’. Pick out correct statement A. Velocity of approach between ( mathrm{P} ) and ( mathrm{Q} ) will be variable. B. Velocity of approach between ( P ) and ( Q ) will be always negative. C. Velocity of approach between ( mathrm{P} ) and ( mathrm{Q} ) will be always constant. D. None of these | 11 |

947 | Define centripetal acceleration. Derive an expression for the centripetal acceleration of a particle moving with uniform speed ‘v’ along a circular path of radius ‘r’. Give the direction of this acceleration. | 11 |

948 | ards north at an angle of 45° to the n travels distance of 4 km towards north at an to the east. How far is the point from the What angle does the straight line joining 12. A car travels 6 km towards north at an east and then travels distance of 4 km angle of 135º to the east. How far is starting point? What angle does the its initial and final position makes with the e (a) 50 km and tan-? (5) (b) 10 km and tan-? (15) (c) 52 km and tan-? (5) (d) 52 km and tan-‘(15) | 11 |

949 | ( m ) | 11 |

950 | A man on a moving cart, facing the direction of motion throws a ball straight up with respect to himself. Which of the following statements is(are) correct? This question has multiple correct options A. The ball will always return to him B. The ball will never return to him. c. The ball will return to him if the cart moves with a constant velocity D. The ball will fall behind him if the cart moves with some acceleration | 11 |

951 | Calculate the angle between two vectors 2F and ( sqrt{2} mathrm{F} ) so that the resultant force is ( mathrm{F} sqrt{10} ) A. 120 degrees B. 90 degrees c. 60 degrees D. 45 degrees | 11 |

952 | The resultant of ( vec{P} ) and ( vec{Q} ) is ( vec{R} ). If ( vec{Q} ) isdoubled, ( vec{R} ) is doubled; when ( vec{Q} ) is reversed, ( overrightarrow{boldsymbol{R}} ) is again doubled. Find ( boldsymbol{P} ) : ( boldsymbol{Q}: boldsymbol{R} ) | 11 |

953 | The resultant of two vectors ( vec{P} ) and ( vec{Q} ) is ( vec{R} ). If the magnitude of ( vec{Q} ) is doubled, the new resultant vector becomes perpendicular to ( vec{P} ). Then, the magnitude of ( overrightarrow{boldsymbol{R}} ) is equal to ( A cdot P+Q ) в. ( P ) c. ( P-Q ) D. ( Q ) | 11 |

954 | The centripetal acceleration of a particle varies inversely with the square of the radius ( r ) of the circular path. The KE of this particle varies directly as: ( A ) B ( cdot r^{2} ) c. ( r^{-} 2 ) D. ( r^{-1} ) | 11 |

955 | A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle The motion of he particle takes place in a plane It follows that A. Its velocity is constant B. Its acceleration is constant C. Its kinetic energy is conserved D. None of these | 11 |

956 | A body has an initial velocity of ( 3 m / s ) and has an acceleration of ( 1 mathrm{ms}^{-2} ) normal to the direction of the initial velocity. Then its velocity ( 4 s ) after the start is A ( cdot 7 m s^{-1} ) along the direction of initial velocity B. ( 7 m s^{-1} ) along the normal to the direction of the initial velocity c. ( 7 m s^{-1} ) mid-way between the two directions D ( cdot 5 m s^{-1} ) at an angle of ( tan ^{-1} frac{4}{3} ) with the direction of the initial velocity | 11 |

957 | A particle is projected at an angle ( theta ) from ground with speed ( uleft(g=10 m / s^{2}right) ) then which of the following is true? This question has multiple correct options A ( cdot ) If ( u=10 m / s ) and ( theta=30^{circ}, ) then time of flight will be 1 ( sec ) B . If ( u=10 sqrt{3} m / s ) and ( theta=60^{circ} ), then time of flight will be ( 3 sec ) C . If ( u=10 sqrt{3} m / s ) and ( theta=60^{circ} ), then after 2 sec velocity becomes perpendicular to initial velocity D. If ( u=10 m / s ) and ( theta=30^{circ} ), then velocity never becomes perpendicular to intial velocity during its flight | 11 |

958 | A stone is thrown from a bridge at an angle of ( 30^{circ} ) down with the horizontal with a velocity of ( 25 m / s ). If the stone strikes the water after 2.5 seconds, then calculate the height of the bridge from the water surface. | 11 |

959 | A point ( P ) moves in counter-clockwise direction on a circular path as shown in the figure. The movement of ( boldsymbol{P} ) is such that it sweeps out a length ( s=t^{2}+5 ) where ( s ) is in metres and ( t ) is in seconds. The radius of the path is ( 20 m ). The acceleration of ( boldsymbol{P} ) when ( boldsymbol{t}=boldsymbol{2} boldsymbol{s} ) is approximately : A ( cdot 13 m / s^{2} ) В. ( 2.15 m / s^{2} ) ( c cdot 7 cdot 2 m / s^{2} ) | 11 |

960 | When a particle moves along a straight path, then the particle has A. tangential acceleration only B. centripetal acceleration only c. both tangential and centripetal acceleration D. none of the mentioned | 11 |

961 | A red cart starts from rest at the top of a ramp and coasts down the ramp with a constant acceleration. A blue motor car starts at the top of the same ramp directly beside the red cart. The blue motor car moves down the ramp with a constant speed. When the red cart catches up to the blue car, how does the speed of the red cart compare with the speed of the blue car? A. The red cart is moving at the same speed as the blue car B. The red cart is moving slightly faster than the blue car c. The red cart is moving more slowly than the blue car D. The red cart is moving twice as fast as the blue car | 11 |

962 | If a body is projected with a velocity of ( 9.8 m / s ) making an angle of ( 45^{circ} ) with the horizontal, then the range of the projectile is (Take ( boldsymbol{g}=mathbf{9 . 8} boldsymbol{m} / boldsymbol{s}^{2} ) ) ( mathbf{A} cdot 39.2 m ) в. ( 9.8 m ) ( mathrm{c} .4 .9 mathrm{m} ) D. ( 19.6 m ) | 11 |

963 | If the vectors ( vec{A}=2 hat{i}+4 hat{j} ) and ( vec{B}= ) ( mathbf{5} hat{mathbf{i}}-boldsymbol{p} hat{boldsymbol{j}} ) parallel to each other, the magnitude of ( bar{B} ) is: A ( 5 sqrt{5} ) 5 B. 10 c. 15 D. ( 2 sqrt{5} ) | 11 |

964 | A body is first displaced by ( 5 mathrm{m} ) and then by ( 12 mathrm{m} ) in different directions. The minimum displacement it can have is ( mathrm{m} ) ( A cdot 7 ) B. 13 ( c .0 ) D. 17 | 11 |

965 | Consider two children riding on the merry-go-round Child 1 sits near the edge, child 2 sits closer to the centre. Let ( v_{1} ) and ( v_{2} ) denote the linear speed of child 1 and child ( 2, ) respectively. Which of the following is true? ( A cdot v_{1}>v_{2} ) В . ( v_{1}=v_{2} ) ( mathrm{c} cdot v_{1}<v_{2} ) D. (4) we cannot determine which is true, without mo nformatio | 11 |

966 | 41. Figure A.20 shows the velocity and acceleration point line body at the initial moment of its motion acceleration vector of the body remains constant. T minimum radius of curvature of trajectory of the body i Vo = 8 ms-1 a = 2 m 526 = 150° Fig. A.20 a. 2 m b. 3 m c. 8 m d. 16 m | 11 |

967 | Find a unit vector in direction of ( overrightarrow{boldsymbol{A}}= ) ( mathbf{5} hat{mathbf{i}}+hat{boldsymbol{j}}-mathbf{2} boldsymbol{k} ) | 11 |

968 | A particle is moving along a circle with uniform speed. The physical quantity which is constant both in magnitude and direction, is A. velocity B. centripetal acceleration c. centripetal force D. angular velocity | 11 |

969 | 1. A particle is projected from the horizontal x-z plane, in vertical x-y plane where x-axis is horizontal and positive y-axis vertically upwards. The graph of ‘y’ coordinate of the particle v/s time is as shown. The range of the particle is 3. Then the speed of the projected particle is: 403 (a) 13 m/ s lid (b) 3 m/s (c) 275 m/s (d) 28 m/s ) | 11 |

970 | onu UBIC CODY Tum 18. A ship is sailing due north at a speed of 1.25 ms. The current is taking it towards east at the rate of 2 ms’ and a sailor is climbing a vertical pole in the ship at the rate of 0.25 ms. Find the magnitude of the velocity of the sailor with respect to ground. 10 1 | 11 |

971 | A smooth ball ‘A’ moving with velocity ‘V’ collides with another smooth initial ball at rest. After collision both the balls move the same speed with angle between their velocities ( 60^{0} . ) No external force acts on the systems of balls. Choose the correct option(s). A ( cdot ) The speed of each ball after the collision is ( frac{V}{sqrt{3}} ) B. The speed of each ball after the collision is ( frac{2 V}{sqrt{3}} ) C. The magnitude of change in momentum of ball B is ( left(frac{m V}{sqrt{3}}right) ) D. The magnitude of change in momentum of ball B is ( left(frac{2 m V}{sqrt{3}}right) ) | 11 |

972 | the Illustration 5.26 Two inclined planes OA and OB having in clination (with horizontal) 30° and 60°, respectively, intersect each other at O as shown in Fig. 5.44. A particle is projected from point P with velocity u=103 ms’ along a direction perpendicular to plane OA. If the particle strikes plane OB perpendicularly at Q, calculate the 3060° Fig. 5.44 a. velocity with which particle strikes the plane OB. b. time of flight. c. vertical height h of P from O. d. maximum height from 0, attained by the particle. e. distance PQ. | 11 |

973 | Which cannonball travels farther? ( A cdot A ) B. B C. Both reaches same height D. cannot be judged | 11 |

974 | 33. A ball is thrown with a velocity whose horizontal component is 12 ms from a point 15 m above the ground and 6 m away from a vertical wall 18.75 m high in such a way so as just to clear the wall. At what time will it reach the ground? (g = 10 ms) | 11 |

975 | The equations of motion of a projectile are given by ( boldsymbol{x}=mathbf{3 6} boldsymbol{t m} ) and ( mathbf{2} boldsymbol{y}=mathbf{9 6} boldsymbol{t}- ) ( 9.8 t^{2} mathrm{m} . ) The angle of projection is ( A cdot sin ^{-1}(4 / 5) ) B. ( sin ^{-1}(3 / 5) ) ( c cdot sin ^{-1}(4 / 3) ) ( D cdot sin ^{-1}(3 / 4) ) | 11 |

976 | A metal piece of mass ( 160 g ) lies in equilibrium inside a glass of water. The pieces touch the glass at small number of point. If the density of the metal is ( 8000 mathrm{kg} / mathrm{m}^{3} ) then the normal force exerted by the bottom of the glass on the metal piece is ( A cdot 2 N ) В. 8 N c. ( 0.16 N ) D. 1.4 | 11 |

977 | A point moves on the ( x-y ) plane according to the law ( x=a sin omega t ) and ( boldsymbol{y}=boldsymbol{a}(mathbf{1}-cos boldsymbol{omega} boldsymbol{t}) ) where ( boldsymbol{a} ) and ( boldsymbol{omega} ) are positive constants and ( t ) is in seconds. Find the distance covered in time ( t_{0} ) A ( . a omega t_{0} ) B. ( sqrt{2 a^{2}+2 a^{2} cos omega t_{0}} ) ( ^{mathrm{C}} 2 a sin frac{omega t_{0}}{2} ) D. ( 2 a cos frac{omega t_{0}}{2} ) | 11 |

978 | The displacement of a particle moving along ( boldsymbol{x} ) axis is given by ( boldsymbol{X}=left(mathbf{4} boldsymbol{t}^{2}+right. ) ( 3 t+7) mu . ) Calculate instantaneous velocity and instantaneous acceleration at ( t=2 S ) | 11 |

979 | For a particle in circular motion the centripetal acceleration should be A. Equal to tangential acceleration B. More than to is tangential acceleration c. Less than to its tangential acceleration D. May be more or less than its tangential acceleration | 11 |

980 | a. 125 . 05 L. 13 2. A man can swim in still water with a speed of 2 ms. If he wants to cross a river of water current speed ✓ along the shortest possible path, then in which direction should he swim? a. At an angle 120° to the water current b. At an angle 150° to the water current c. At an angle 90° to the water current d. None of these mit of 54 mb-1 | 11 |

981 | Q Type your question- car has a constant speed corresponding to a normal acceleration of ( 8 m / s^{2} ) The tracks abcde and ( 2 C 3 ) are semicircular track while tracks ( 1-2 ) and ( 3-4 ) are straight track Point ( a ) and point 1 are the starting point of race and point 4 and point e are finishing point of race and point 4 and point ( e ) are finishing point of the race Choose the correct statements A ( cdot ) Car A wins the race with time difference ( frac{14+3}{3} s ) B. car A wins the race with time difference ( frac{14-3}{3} ) C car B wins the race with time difference ( frac{14+3}{3} s ) D. car B wins with the race with time difference ( frac{14-3}{3} s ) | 11 |

982 | A boy can throw a stone up to maximum height of 10cm. The maximum horizontal distance that the boy can throw the same stone up to will be? | 11 |

983 | A projectile is fired with a velocity at right angle ( theta ) to the slope which is inclined at an angle ( theta ) with the horizontal. The expression for the range ( boldsymbol{R} ) along the incline is: ( ^{mathbf{A}} cdot frac{2 v^{2}}{g} sec theta ) B ( cdot frac{2 v^{2}}{g} tan theta ) ( ^{mathrm{c}} cdot frac{2 v^{2}}{g} sec theta tan theta ) D ( cdot frac{2 v^{2}}{g} tan ^{2} theta ) | 11 |

984 | Find the horizontal velocity of the particle when it reach the point ( Q ) Assume the block to the frictionless. take ( boldsymbol{g}=mathbf{9 . 8 m} / boldsymbol{s}^{2} ) A ( cdot v=3.13 frac{m}{s} ) B. ( 5 mathrm{m} / mathrm{s} ) c. ( sqrt{g} mathrm{m} / mathrm{s} ) D. ( 3.6 mathrm{m} / mathrm{s} ) | 11 |

985 | и мышvмvv v v vvрисеппопол Спо опи. 6. Find the vector sum of N coplanar forces, each of magnitude F, when each force makes an angle of 21t/N with that preceding it. | 11 |

986 | murun me SUMI U. UVIUM d with the same speed but making 46. Two stones are projected with the same speed but erent angles with the horizontal. Their ranges are equal. If the angle of projection of one is t3 and its maximum height is h, then the maximum height of the other be a. 37 b. 2h c. 1,12 d. h,13 | 11 |

987 | 2. A particle is projected from a point (0, 1) on Y-axis (assume + Y direction vertically upwards) aiming towards a point (4,9). It fell on ground along x axis in 1 sec. Taking g = 10 m/s2 and all coordinate in metres. Find the X-coordinate where it fell. (a) (3,0) (b) (4,0) (c) (2,0) (d) (273,0) | 11 |

988 | A particle is going with constant speed along a uniform helical and spiral path separately as shown in figure then Essume that the vertical acceleration | 11 |

989 | For three non-zero vectors ( vec{a}, vec{b}, vec{c} ) the elation ( |(vec{a} times vec{b}) cdot vec{c}|=|vec{a}||vec{b}||vec{c}| ) will hold true if and only if: ( mathbf{A} cdot vec{a} cdot vec{b}=0, vec{b} cdot vec{c}=0 ) В . ( vec{c} . vec{a}=0, vec{a} . vec{b}=0 ) C ( . vec{a} . vec{c}=0, vec{b} . vec{c}=0 ) D. ( vec{a} . vec{b}=vec{b} . vec{c}=vec{c} . vec{a}=0 ) | 11 |

990 | 21. At the point where the particle is at a height half of maximum height H attained by it 2u? (1+cos e)/2 u? (1 + cos? 0)3/2 82√2 coso 82/2 cos ?(1-sin’0)3/2 u? (1-tane)3/2 8272 cos 8 V2 cos e | 11 |

991 | The time after which bolt hit the floor of the elevator | 11 |

992 | Assertion In projectile motion at any two positions ( frac{overrightarrow{boldsymbol{v}}_{2}-overrightarrow{boldsymbol{v}}_{1}}{boldsymbol{t}_{2}-boldsymbol{t}_{1}} ) always remains constant. Reason The given quantity is average acceleration, which should remain constant as acceleration is constant A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion is incorrect but Reason is correct | 11 |

993 | Rain appears to fall vertically to a man walking at ( 3 k m h^{-1}, ) but when he changes his speed to double, the rain appears to fall at ( 45^{circ} ) with vertical Study the following statements and find which of them are correct. | 11 |

994 | Which of the sport is most affected by variation of ‘g’? A. swimming B. jump c. horse riding D. shooting E. all are equally affected | 11 |

995 | Two cars 1 and 2 move with velocities ( v_{1} ) and ( v_{2} ) respectively, on a straight road in same direction. When the cars are separated by a distance d, the driver of car 1 applies brakes and the car moves with uniform retardation ( a_{1} ) Simultaneously, car 2 starts accelerating with ( a_{2} ). If ( v_{1}>v_{2} ). Find the minimum initial separation between the cars to avoid collision between them. | 11 |

996 | A ( 100 m ) long train at ( 15 m / s ) overtakes a man running on the platform in the same direction in ( 10 s . ) How long the train will take top cross the man if he was running in the opposite direaction? A . ( 7 s ) B. 5 s ( c .3 s ) D. ( 1 s ) | 11 |

997 | A particle moves uniformly in a circle of radius ( 25 mathrm{cm} ) at two revolution per second. Find the acceleration of the particle in ( boldsymbol{m} / boldsymbol{s}^{2} ) | 11 |

998 | When a man moves down the inclined plane with a constant speed ( 5 m s^{-1} ) which makes an angle of ( 37^{circ} ) with the horizontal, he finds that the rain is falling vertically downward. When he moves up the same inclined plane with the same speed, he finds that the rain makes an angle ( theta=tan ^{-1}left(frac{7}{8}right) ) with the horizontal. The speed of the rain is A ( cdot sqrt{116} mathrm{ms}^{-1} ) B. ( sqrt{32} mathrm{ms}^{-1} ) c. ( 5 m s^{-1} ) D. ( sqrt{73} mathrm{ms}^{-1} ) | 11 |

999 | An athlete completes one round of a circular track of diameter ( 200 mathrm{m} ) in 40 s. What will be the distance covered and also the displacement at the end of 2 ( min 20 s ? ) | 11 |

1000 | muzzle speed UI UNTUT IT 32. Figure 5.196 shows an elevator cabin, which is movin downwards with constant acceleration a. A particle projected from corner A, directly towards diagonally opposite corner C. Then prove that Fig. 5.196 a. Particle will hit C only when a = 8. b. Particle will hit the wall CD if a g. | 11 |

1001 | 9. Ship A is located 4 km north and 3 km east of ship B. Ship A has a velocity of 20 kmh-‘ towards the south and ship B is moving at 40 km h-‘ in a direction 37° north of east. Take x- and y-axes along east and north directions, respectively. a. Velocity of A relative to B is -32i – 44j. b. Position of A relative to B as a function of time is given by FAB = (3 – 32t)î + (4 – 44t)ſ where t = 0 when the ships are in position described above. c. Velocity of B relative to A is -32 – 44ſ. d. At some moment A will be west of B. | 11 |

1002 | The length of a seconds hand in a watch is ( 1 mathrm{cm} . ) The change in its velocity in 15 s is A. ( 0 mathrm{cm} / mathrm{s} ) B. ( frac{pi}{30 sqrt{2}} mathrm{cm} / mathrm{s} ) c. ( frac{pi}{30} mathrm{cm} / mathrm{s} ) D. ( frac{pi}{30} sqrt{2} mathrm{cm} / mathrm{s} ) | 11 |

1003 | A carrom board (4ft ( times 4 ) ft square) has the queen at the centre. The queen, hit by the stricker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen from the centre to the hole. | 11 |

1004 | A particle moves along the side ( A B, B C ) CD of a square of side 25 m with a velocity of 15 m/s. Its average velocity is A ( .15 mathrm{m} / mathrm{s} ) в. ( 10 mathrm{m} / mathrm{s} ) ( mathrm{c} .7 .5 mathrm{m} / mathrm{s} ) D. ( 5 mathrm{m} / mathrm{s} ) | 11 |

1005 | The tip of seconds’ hand of a watch exhibits uniform circular motion on the circular dial of the watch State whether given statement is True/False? A. True B. False | 11 |

1006 | Pictured above are four disks rotating counter-clockwise (as viewed from above) at a constant speed. Which disk is experiencing greatest acceleration? A. green B. red c. blue D. yellow E. All disks are experiencing the same acceleration | 11 |

1007 | 5. The speed of rain with respect to the stationary man is a. 0.5 b. 1.0 ms c. 0.5 v3 ms-1 d. 0.43 ms-1 | 11 |

1008 | A force ( F=5 t ) is applied on a block of mass ( 10 mathrm{kg} ) kept on rough horizontal surface ( (mu=0.5), ) in rest what is speed of the block at ( t=20 ) s? ( A cdot 15 mathrm{m} / mathrm{s} ) B. ( 18 mathrm{m} / mathrm{s} ) ( c cdot 2.5 mathrm{m} / mathrm{s} ) D. cannot be calculated | 11 |

1009 | A boat travels from south bank to north bank of a with a maximum speed of 8 km/h. To arrive at a opposite to the point of start, the boat should start angle : ( mathbf{A} cdot tan ^{-1}(1 / 2) W ) of ( mathrm{N} ) B. ( tan ^{-1}(1 / 2) N ) of ( w ) c. ( 30^{circ} mathrm{WofN} ) D. ( 30^{circ} ) Nof ( W ) | 11 |

1010 | Motion of satellite around the earth is A. retarded B. accelerated c. diverted D. None | 11 |

1011 | Two trains ( A ) and ( B ) of length ( 400 m ) each are moving on two parallel tracks with a uniform speed of ( 72 mathrm{km} / mathrm{h} ) in the same direction, with ( A ) ahead of ( B ) decides to overtake ( A ) and accelerates by ( 1 m / s^{2} . ) If after ( 50 s ) the guard of ( B ) just brushes past the driver of ( A ), what was the original distance between the guard of ( boldsymbol{B} & ) driver of ( boldsymbol{A} ) ? | 11 |

1012 | the net displacement and distance travelled by the bolt, with respect to earth. (Take ( left.g=9.8 m / s^{2}right) ) | 11 |

1013 | 1. A particle is projected from the ground at an angle 30 with the horizontal with an initial speed 20 ms. After how much time will the velocity vector of projectile de perpendicular to the initial velocity? [in second] flicht 80 m to stones are | 11 |

1014 | Illustration 5.34 Two roads intersect at right angle; one goes along the x-axis, another along the y-axis. At any instant, two cars A and B moving along y and x directions, respectively, meet at intersection. Draw the direction of the motion of car A as seen from car B. Car A Car A 7 VB Car B Fig. 5.65 | 11 |

1015 | Two vectors, each of magnitude ( A ) have a resultant of same magnitude ( A ). The angle between the two vectors is ( A cdot 30 ) B. ( 60^{circ} ) ( c cdot 120^{circ} ) D. 150 | 11 |

1016 | A person is sitting on a moving train and is facing the engine. He tosses up a coin which falls behind him. The train is moving: This question has multiple correct options A. forward and gaining speed. B. forward and losing speedd c. backward and losing speed D. backward and gaining speed. | 11 |

1017 | 10. The maximum separation between the floor of elevat and the ball during its flight would be a. 30 m b. 15 m c. 7.5 m d. 9.5 m | 11 |

1018 | Find the magnitude of the angular acceleration at the moment ( t=10.0 s ) A. ( 1.3 mathrm{rad} / mathrm{s} ) B. 3 rad / ( s ) c. 1 rad ( / s ) D. ( 0.3 mathrm{rad} / mathrm{s} ) | 11 |

1019 | Two particles start moving from the same position on a circle of radius 20 ( mathrm{cm} ) with speed ( 40 pi mathrm{m} / mathrm{s} ) and ( 36 pi mathrm{m} / mathrm{s} ) respectively in the same direction. Find the time after which the particles will meet again. | 11 |

1020 | Two roads intersect at right angle; one goes along the ( x ) -axis, another along the y-axis. At any. two cars ( A ) and ( B ) moving along ( boldsymbol{y} ) and ( boldsymbol{x} ) directions; respectively, meet at intersection. Draw the direction of the motion of car ( A ) as seen from car ( boldsymbol{B} ) | 11 |

1021 | Find the distance scovered by the particle during the first 4.0 and ( 8.0 s ) A. ( 3 c m ) B. ( 5 mathrm{cm} ) ( mathrm{c} cdot 10 mathrm{cm} ) D. ( 15 mathrm{cm} ) | 11 |

1022 | The displacement ( x ) of a particle varies with time ( t ) as ( x=a e^{-alpha t}+b e^{beta t}, ) where ( a, b, alpha ) and ( beta ) are positive constants. The velocity of the particle will A. be independent of ( alpha ) and ( beta ) B. drop to zero when ( alpha=beta ) c. go on decreasing with time D. go on increasing with time | 11 |

1023 | 15. Three forces P, Q and R are acting on a particle in the plane, the angle between P and Q & Q and R are 150° and 120° respectively. Then for equilibrium, forces P, Q and R are in the ratio (a) 1:2:3 (b) 1:2: 13 (c) 3:2:1 (d) 13:2:1 | 11 |

1024 | Je and position udents have anot be true 12. Figure A.21 shows path followed by a particle and po of a particle at any instant. Four different students represented the velocity vectors and acceleration vect at the given instant. Which vector diagram cannot be in any situation? (In each figure velocity is tangential the trajectory). Trajectory of PL particle L.90 60 > 90° /04 I Particle at a 0>99 Sita given instant A Ram Fig. A.21 a. Sita b. Gita c. Ram d. Shyam Shyan | 11 |

1025 | The angular displacement of an object having uniform circular motion is ( frac{pi}{4} ) rad in every 3 s.Find the frequency of revolution. | 11 |

1026 | 51. There are two values of time for which a projectile is al the same height. The sum of these two times is equal to (T = time of flight of the projectile) a. 3 T/2 b. 4 T/3 c. 3 T/4 d. T | 11 |

1027 | The displacement ( x ) of a particle at time t is given by ( boldsymbol{x}=boldsymbol{A} boldsymbol{t}^{2}+boldsymbol{B} boldsymbol{t}+boldsymbol{C} ) where ( boldsymbol{A} ) B, ( C ) are constants and ( v ) is velocity of a particle, then the value of ( 4 A x-v^{2} ) is: ( mathbf{A} cdot 4 A C+B^{2} ) В. ( 4 A C-B^{2} ) c. ( 2 A C-B^{2} ) D. ( 2 A C+B^{2} ) | 11 |

1028 | 24. A cubical box dimension L = 5/4 m starts moving with an acceleration a=0.5 ms from the state of rest. At the same time, a stone is thrown from the origin with velocity v =v, i + v, -yk with respect to earth. Acceleration due to gravity g = 10 ms (-)). The stone just touches the roof of box and finally falls at the diagonally opposite point. then: b. v, = 5 | C Vi= d. 13 | 11 |

1029 | 1. A radius vector of point A relative to the origin varies with time t as ř = at i-bt’ſ where a and b are constants. Find the equation of point’s trajectory. mi- | 11 |

1030 | A machine gun is mounted on the top of a tower 100 m high. At what angle should the gun be inclined to cover a maximum range of firing on the ground below? The muzzle speed of bullet is ( 150 m s^{-1} . ) Take ( g=10 m s^{-2} ) | 11 |

1031 | toppr Q Type your question aimed towards ( Q ) and velocity ( vec{u} ) of ( Q ) is perpendicular to ( vec{v} ). The two projectiles meet at time ( boldsymbol{T}= ) ( A ) B. [ frac{(v+u) d}{v^{2}} ] ( c ) [ frac{v(v-u)}{d} ] D. [ frac{v d}{left(v^{2}-u^{2}right)} ] | 11 |

1032 | A particle of mass ( mathrm{m} ) is moving in a circular path of constant radius r such that centripetal acceleration is varying with time ( t ) as ( k^{2} r t^{2}, ) where ( k ) is a constant. The power delivered to the particle by the force acting on it is A ( cdot m^{2} k^{2} r^{2} t^{2} ) B. ( m k^{2} r^{2} t ) ( mathbf{c} cdot m k^{2} r t^{2} ) ( mathbf{D} cdot m k r^{2} t ) | 11 |

1033 | A mass is attached to the end of a string of which is tied to a fixed point 0 The mass is released from the initial horizontal position of the string. Below the point 0 at what minimum distance a peg ( P ) be should fixed so that the mass tums about ( P ) and can describe a complete circle in the vertical plane? A ( cdotleft(frac{3}{5}right) l ) B・(frac{2 } { 5 } ) ( c ) ( D cdot frac{2}{3} ) | 11 |

1034 | Write vector relation between angular velocity ( (vec{omega}), ) tangential velocity ( (vec{V}) ) and position vector ( (vec{r}) ) | 11 |

1035 | A boat is moving with a velocity ( vec{v}= ) ( mathbf{3} hat{mathbf{i}}+mathbf{4} hat{mathbf{j}} ) with respect to ground. The water in the river is moving with a velocity ( vec{u}=-3 hat{i}-4 hat{j} ) with respect to ground. The relative velocity of boat with respect to water is : A ( .6 hat{i}+8 hat{j} ) B. c. ( 6 hat{i}-8 hat{j} ) D. ( -6 hat{i}+8 hat{j} ) | 11 |

1036 | State whether the given statement is True or False : A uniform linear motion is unaccelerated, while a uniform circular motion is an accelerated motion A. True B. False | 11 |

1037 | 20. A particle is projected from ground at some angle with the horizontal. Let P be the point at maximum height At what height above the point P should the particle he aimed to have range equal to maximum height? a. H b. 2H c. H/2 d. 3H | 11 |

1038 | Obtain the relation between the magnitude of linear acceleration and angular acceleration in circular motion. | 11 |

1039 | Define uniform circular motion. | 11 |

1040 | A point moves along a circle having a radius ( 20 c m ) with a constant tangential acceleration ( 5 mathrm{cm} s^{-2} . ) How much time is needed after motion begins for the normal acceleration of the point to be equal to tangential acceleration? A . ( 1 mathrm{s} ) B. 2 ( c cdot 3 s ) D. 4 s | 11 |

1041 | A body is projected with velocity ( 24 m s^{-1} ) making an angle ( 30^{circ} ) with the horizontal. The angle made by the direction of the projectile with the horizontal at ( 2 s ) from start is: A ( cdot tan ^{-1} frac{2}{3 sqrt{3}} ) B. ( tan ^{-1} frac{1}{3 sqrt{3}} ) c. ( tan ^{-1} frac{2}{3} ) D. ( tan ^{-1} frac{1}{3} ) | 11 |

1042 | Three point masses ( m_{1}, m_{2} ) and ( m_{3} ) are located at the vertices of an equilateral triangle of length ( a ). Determine the moment of inertia of the system anout an axis along the altitude of the triangle passing through ( boldsymbol{m}_{1} ) | 11 |

1043 | In Uniform circular motion direction of velocity is along the drawn to the position of particle on the circumference of the circle. A. normal B. tangent c. can be both D. none of these | 11 |

1044 | A projectile shot at an angle of ( 45^{circ} ) above the horizontal strikes the wall of a building ( 30 m ) away at a point ( 15 m ) above the point of projection. Initial velocity of the projectile is ( left(operatorname{take} g=9.8 m / s^{2}right) ) ( mathbf{A} cdot 14 m / s ) B. ( 14 sqrt{2} mathrm{m} / mathrm{s} ) c. ( 14 sqrt{3} mathrm{m} / mathrm{s} ) D. ( 14 sqrt{5} mathrm{m} / mathrm{s} ) | 11 |

1045 | 11. A particle moves in a circle of radius 20 cm. Its linear speed is given by v = 2t where t is in seconds and v in ms. Then a. The radial acceleration at t = 2 s is 80 ms. b. Tangential acceleration at t = 2 s is 2 ms. c. Net acceleration at t = 2 s is greater than 80 ms d. Tangential acceleration remains constant in magnitude. | 11 |

1046 | 5. A projectile A is projected from ground. An observer B running on ground with uniform velocity of magnitude ‘v’ observes A to move along a straight line. The time of flight of A as measured by B is T. Then the range R of projectile on ground is (a) R=VT (b) RvT (d) information insufficient to draw inference | 11 |

1047 | A ball thrown by your friend towards you, undergoes: A. curvilinear motion B. linear motion c. rotational motion D. projectile motion | 11 |

1048 | 3. Forces F, and F2 act on a point mass in two mutually perpendicular directions. The resultant force on the point mass will be (a) Fi + F2 (b) F,-F2 (c) VF+ F2 (d) F? + F2 | 11 |

1049 | In a uniform circular motion (horizontal) of a ball tied with a string, velocity at any time is at an angle, ( boldsymbol{theta} ) with acceleration. Then ( boldsymbol{theta} ) is: A ( cdot 60^{circ} ) B. ( 30^{circ} ) ( c .90^{circ} ) D. none of the above | 11 |

1050 | Given that ( vec{P}+vec{Q}=vec{P}-vec{Q} ). This can be true when :- A ( cdot vec{P}=vec{Q} ) B . ( vec{Q} ) is a null vector C. Niether ( vec{P} ) and ( vec{Q} ) is a null vector D. ( vec{P} ) is perpendicular to ( vec{Q} ) | 11 |

1051 | u. OSOITIE INIMICITIA WII UE WESL OID. 10. An object moves with constant acceleration ā. Which of the following expressions is/are also constant? – dt dt dullil ed(v²) dt dt | 11 |

1052 | Resolve a weight of ( 10 N ) in two directions which are parallel and perpendicular to a slope inclined at ( 30^{circ} ) to the horizontal. | 11 |

1053 | To a man walking at the rate of ( 3 k m / h ) the rain appears to fall vertically. When he increases his speed to ( 6 k m / h ) it appears to meet him at an angle of ( 45^{circ} ) with vertical. The speed of rain is ( mathbf{A} cdot 2 sqrt{2} k m / h ) B. ( 3 sqrt{2} mathrm{km} / mathrm{h} ) ( mathrm{c} cdot 2 sqrt{3} mathrm{km} / mathrm{h} ) D. ( 3 sqrt{3} mathrm{km} / mathrm{h} ) | 11 |

1054 | Two ships ( A ) and ( B ) are ( 10 k m ) apart on a line running south to north. Ship ( boldsymbol{A} ) farther north is streaming west at ( 20 k m / h r ) and ship ( B ) is streaming north at ( 20 k m / h r . ) What is their distance of closest approach and how long do they take to reach it? A. ( 4 sqrt{2} mathrm{km}, 15 mathrm{min} ) В. ( 5 sqrt{5} ) km, 15 min c. ( 5 sqrt{2} mathrm{km}, 20 mathrm{min} ) D. ( 2 sqrt{2} mathrm{km}, 15 mathrm{min} ) | 11 |

1055 | A car runs at constant speed on a circular track of radius ( 100 mathrm{m} ) taking ( 62.8 mathrm{s} ) on each lap. What is the average speed and average velocity on each complete lap? ( (boldsymbol{pi}=mathbf{3 . 1 4}) ) A. Velocity 10 ( mathrm{m} / mathrm{s} ), speed ( 10 mathrm{m} / mathrm{s} ) B. Velocity zero, speed 10 m/s c. Velocity zero, speed zero D. Velocity 10 ( mathrm{m} / mathrm{s} ), speed zero | 11 |

1056 | A particle is travelling along a straight line ( O X . ) The distance ( x ) (in metre) of the particle from ( boldsymbol{O} ) at a time ( ^{prime} boldsymbol{t}^{prime} ) is given by ( boldsymbol{x}=mathbf{3 7}+mathbf{2 7 t}-boldsymbol{t}^{3}, ) where ‘t’ is time in second. The distance of the particle from ( O ),when it comes to rest is: A. ( 81 m ) в. ( 91 m ) c. ( 101 m ) D. ( 111 m ) | 11 |

1057 | Assertion In the motion of projectile the horizontal component of velocity remains constant Reason The force on the projectile is gravitational force which acts only in vertically downward direction A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

1058 | The motion of the arm of a fast bowler while bowling is an example of nonuniform circular motion. State whether given statement is True/False? | 11 |

1059 | Find the ( x ) coordinate of the particle at the moment of time ( t=6 s ) ( mathbf{A} cdot x=0.4 m ) B. ( x=0.24 m ) c. ( x=0.42 mathrm{m} ) D. ( x=0.44 mathrm{m} ) | 11 |

1060 | 7. A river is flowing from west to east at a speed of 5 m min. A man on the south bank of the river, capable of swimming at 10 m minin still water, wants to swim across the river in the shortest time. Finally, he will move in a direction a. tan-(2) E of N b. tan- (2) N of E c. 30° E of N d. 60° E of N | 11 |

1061 | If the range of a gun which fires a shell with muzzle speed ( v ), is ( R ), then the angle of elevation of the gun is ( ^{mathbf{A}} cdot cos ^{-1} frac{v^{2}}{R g} ) B. ( cos ^{-1} frac{R g}{v^{2}} ) c. ( frac{1}{2} sin ^{-1} frac{v^{2}}{R g} ) D. ( frac{1}{2} sin ^{-1} frac{R g}{v^{2}} ) | 11 |

1062 | Two boys are standing at the ends ( A ) and B of a ground, where ( A B=a ). The boy at ( B ) starts running in a direction perpendicular to AB with velocity ( v_{1} ). The boy at A starts running simultaneously with velocity ( v ) and catches the other boy in a time ( t, ) where ( t ) is A. ( frac{a}{sqrt{v^{2}+v_{1}^{2}}} ) в. ( sqrt{frac{a^{2}}{v^{2}-v_{1}^{2}}} ) c. ( frac{a}{left(v-v_{1}right)} ) D. ( frac{a}{left(v+v_{1}right)} ) | 11 |

1063 | A student is standing at a distance of ( mathbf{5 0} ) meters behind a bus. As soon as the bus starts with an acceleration of ( 1 m s^{-2}, ) the student starts running towards the bus with a uniform velocity ( u ). Assuming the motion to be along straight road the minimum value of ( u ) so that the student is able to catch the bus is: A ( .5 mathrm{ms}^{-1} ) B. ( 8 m s^{-1} ) ( mathrm{c} cdot 10 mathrm{ms}^{-1} ) D. ( 12 mathrm{ms}^{-1} ) | 11 |

1064 | 4. In Q. 1, what would be the approximate retardation to be given by jet pack along for safe landing? a. 58 ms b. 2g ms c. 4g ms-2 d. Cannot be determined | 11 |

1065 | Q Type your question speed ( v ) in such a way that ( K ) always moves directly towards ( L, L ) directly moves towards ( M, M ) directly towards ( N ) and ( N ) directly towards ( K . ) The four persons will meet at time ( t= ) ( ^{A} cdot underline{4 d} ) ( v ) в. ( frac{3 d}{v} ) c. ( frac{2 d}{v} ) ( D cdot d ) | 11 |

1066 | 2. A=2ỉ +ì, B = 3j – k and © = 6ỉ – 2k . Value of A-2B+ 3C would be (a) 20î +59 + 4Â (b) 20î – 5 – 4Â (c) 4 +59 + 20 (d) si + 4 + 10k | 11 |

1067 | toppr Q Type your question. as shown. At the same instant, a man ( P ) throws a ball vertically upwards with initial velocity ‘ ( u^{prime} ). Ball touches (coming to rest) the base of the plane at point ( B ) of plane’s journey when it is vertically above the mans. ‘ ( s^{prime} ) is the distance of point ( B ) from point ( A ). Just after the contact of ball with the plane, acceleration of plane increases to ( 3 m / s^{2} . ) Find: (i) Initial velocity ( ^{prime} u^{prime} ) of ball. (ii) Distance ( ^{prime} s^{prime} ) (iii) Distance between man and plane when the man catches the ball black. ( left.boldsymbol{g}=mathbf{1 0} boldsymbol{m} / boldsymbol{s}^{2}right) ) (Neglect the height of ( operatorname{man}) ) | 11 |

1068 | A man crosses the river, perpendicular to river flow in time ( t ) seconds and travels an equal distance down the stream in ( T ) second. The ratio of man’s speed in still water to the speed of river water will be: ( ^{A} cdot frac{t^{2}-T^{2}}{t^{2}+T^{2}} ) в. ( frac{T^{2}-t^{2}}{T^{2}+t^{2}} ) c. ( frac{t^{2}+T^{2}}{t^{2}-T^{2}} ) D. ( frac{T^{2}+t^{2}}{T^{2}-t^{2}} ) | 11 |

1069 | Two projectile ( A ) and ( B ) thrown with speed in the ratio acquired the same heights.If A is thrown at an angle of projection of B will be. | 11 |

1070 | 16. The position vectors of two balls are given by ĩ = 2(m)i+7(m); F = -2(m)i + 4(m); What will be the distance between the two balls? 1.50 -1 | 11 |

1071 | Two paper screens A and B are separated by 150 m. A bullet pierces A and B. The hole in B is 15 cm below the hole in A. If the bullet is travelling horizontally at the time of hitting A, then the velocity of the bullet at A is (8 = 10 ms-2) a. 100 V3 ms -1 b. 200 V3 ms-1 c. 300 V3 ms d. 500 V3 ms -1 og of | 11 |

1072 | Linear ( & ) Angular acceleration of a particle is ( 10 mathrm{m} / mathrm{sec}^{2} ) and ( 5 mathrm{rad} / mathrm{sec}^{2} ) respectively. What is its from rotational axis : A . ( 50 m ) B. ( 1 / 2 m ) ( c .1 m ) D. ( 2 m ) | 11 |

1073 | Find a unit vector in the direction of ( overrightarrow{A B} ) where ( A(1,2,3) ) and ( B(4,5,6) ) are the given points. | 11 |

1074 | The motion of a particle is described by the equation ( boldsymbol{x}=boldsymbol{a}+boldsymbol{b} boldsymbol{t}^{2} ) where ( boldsymbol{a}= ) ( 15 mathrm{cm} ) and ( b=3 mathrm{cm} / mathrm{sec}^{2} . ) Its instantaneous velocity at time 3 sec will be: A. ( 36 mathrm{cm} / mathrm{sec} ) B. ( 1 mathrm{cm} / mathrm{sec} ) c. ( 18 mathrm{cm} / mathrm{sec} ) D. ( 32 mathrm{cm} / mathrm{sec} ) | 11 |

1075 | 36. Figure 6.16 show that particle A is B projected from point P with velocity PK u along the plane and simultaneously another particle B with velocity v at an angle a with vertical. The particles collide at point Q on the plane. Then a. v sin (a -0.) = u b. v cos (a- .) = u c. V = u d. None of these | 11 |

1076 | A body is projected horizontally from a height of ( 78.4 m ) with a velocity ( 10 m s^{-1} ) Its velocity after 3 seconds is ( ( boldsymbol{g}=mathbf{1 0 m s}^{-1} ) ). (Take direction of projection on ( hat{i} ) and vertically upward direction on ( hat{j} ) ): ( mathbf{A} cdot 10 hat{i}-30 hat{j} ) B. ( 10 hat{i}+30 hat{j} ) c. ( 20 hat{i}-30 hat{j} ) D. ( 10 hat{i}+10 sqrt{30} hat{j} ) | 11 |

1077 | A uniform disk rotating with constant angular acceleration covers 50 revolutions in the first five seconds after the start. Calculate the angular acceleration and the angular velocity at the end of five seconds. | 11 |

1078 | If ( vec{A}=vec{B}+vec{C}, ) and the magnitudes of ( vec{A} ) ( vec{B}, vec{C} ) are ( 5,4, ) and 3 units, then the angle between ( vec{A} ) and ( vec{C} ) is A ( cdot cos ^{-1}left(frac{3}{5}right) ) B. ( cos ^{-1}left(frac{4}{5}right) ) ( ^{c} cdot sin ^{-1}left(frac{3}{4}right) ) D. ( frac{pi}{2} ) | 11 |

1079 | A body of mass m is projected horizontally with a velocity from the top of a tower of height h and it reaches the sround at a distance x from the foot of the tower. If a second body of mass 2 m is projected horizontally from the top of a tower of height 2 h, it reaches the ground at a distance 2x from the foot of the tower. The horizontal velocity of the second body is a. v b. 2v in c. /2v d. vl2 . 1. conto11- 1- | 11 |

1080 | The flow speeds of air on the lower and upper surfaces of the wing of an aeroplane are ( v ) and respectively.The density of air is ( mathrm{p} ) and surface area of wings is A.The dynamic lift on the wing is- | 11 |

1081 | A cannon fires successively two shells with velocity ( v_{0}=250 m / s ; ) the first at the angle ( theta_{1}=60^{circ} ) and the second at the angle ( theta_{2}=45^{circ} ) to the horizontal, the azimuth being the same. Neglecting the air drag, the time interval(in seconds) between firings leading to the collision of the shells is ( (10+x) ). Find the value of x. (Take ( g=10 m / s^{2} ) and round-off your answer to the nearest integer.) | 11 |

1082 | 17. Two boats bo passengers in it o boats both having a mass of 150 kg including engers in it are at rest. A sack of mass 50 kg makes + boat having total mass of 200 kg. It is thrown to the rond boat with a velocity whose horizontal component ms-1. relative to water. Calculate the distance (in m) hetween the boat 8.5 s. after the throw if the sack spent 0.5 s. in air. Neglect the resistance of air and water. | 11 |

1083 | car is moving horizontally along a straight line with uniform velocity of 25 ms. A projectile is to be fired from this car in such a way that it will return to it after it has moved 100 m. The speed of the projection must be 10 ms b. 20 ms c. 15 ms’ d. 25 ms 10 ondamn: | 11 |

1084 | Two bodies move uniformly towards each other. They become ( 4 m ) nearer in every 1 second. After crossing each other they get ( 4 m ) farther every 10 second. If their speeds are constant, their values would be A . ( 1.8 m s^{-1}, 1.8 m s^{-1} ) B . ( 2.2 m s^{-1}, 2.0 m s^{-1} ) c. ( 2.2 m s^{-1}, 1.8 m s^{-1} ) D. ( 1.5 m s^{-1}, 2.5 m s^{-1} ) | 11 |

1085 | Show that the area of the triangle contained between the vectors a and b is one half of the magnitude of ( a times b ) | 11 |

1086 | Illustration 4.2 A particle moves in x-y plane such that its position vector varies with time as ř= (2 sin 3t)i +2(1-сos 3t)j. Find the equation of the trajectory of the particle. | 11 |

1087 | Co-efficient of restitution is defined as the ratio of A. Velocity of separation and approach B. Velocity of approach and separation c. Ratio of velocity of objects D. None | 11 |

1088 | A particle is moving along a circular path with a constant speed of ( 10 m s^{1} ) What is the magnitude of the change is velocity of the particle, when it moves through an angle of 60 around the centre of the circle? A . в. ( 10 mathrm{m} / mathrm{s} ) ( mathbf{c} cdot 10 sqrt{3} m / s ) D. ( 10 sqrt{2} mathrm{m} / mathrm{s} ) | 11 |

1089 | Fig. 5.66 Illustration 5.35 Two roads one, along the y-axis and anoth along a direction at angle with x-axis, are as shown in F 5.68. Two cars A and B are moving along the roads. Consid the situation of the diagram. Draw the direction of VR Road Car A Car B Fig. 5.68 a. Car B as seen from car A. b. Car A as seen from car B. | 11 |

1090 | If ( vec{a}=2 hat{i}+4 hat{j}-5 hat{k}, vec{b}=hat{i}+ ) ( hat{boldsymbol{j}}+hat{boldsymbol{k}}, overrightarrow{boldsymbol{c}}=hat{boldsymbol{j}}+2 hat{boldsymbol{k}}, ) then the unit vectors parallel to ( overrightarrow{boldsymbol{a}}+overrightarrow{boldsymbol{b}}+overrightarrow{boldsymbol{c}} ) is A ( cdot pm frac{1}{7}(3 hat{i}+6 hat{j}-2 hat{k}) ) в. ( (3 hat{i}+6 hat{j}-2 hat{k}) ) ( ^{mathrm{C}} pm frac{1}{7}(3 hat{i}+6 hat{j}+2 hat{k}) ) D. ( (3 hat{i}+6 hat{j}+2 hat{k}) ) | 11 |

1091 | Illustration 5.28 A body is thrown at an angle e, with the horizontal such that it attains a speed equal to times the speed of projection when the body is at half of its maximum height. Find the angle 8. | 11 |

1092 | Q Type your question. moving horizontally with a speed ( u ) perpendicular to the direction of ( v ) enters through a hole at an upper corner ( A ) and strikes the diagonally opposite corner ( B ). Assume ( g=10 m / s^{2} . ) Which of the following values of ( u ) and ( v ) is(are) correct? This question has multiple correct options A. ( v=20 mathrm{m} / mathrm{s} ) в. ( u=3 mathrm{m} / mathrm{s} ) c. ( v=15 mathrm{m} / mathrm{s} ) D. ( u=2 m / s ) | 11 |

1093 | 4. The trajectory of a projectile in a vertical plane is y = ax – bx’. where a, b are constants, and x and y are, respectively, the horizontal and vertical distances of the projectile from the point of projection. The maximum height attained is and the angle of projection from the horizontal (IIT JEE, 1997) | 11 |

1094 | A drunkard is walking along a straight road. He takes 5 steps forward and 3 steps backward and so on. Each step is 1 ( mathrm{m} ) long and takes 1 s. There is a pit on the road 11 m away from the starting point. The drunkard will fall into the pit after: A . 21 s B. 29 s c. ( 31 s ) D. 37 s | 11 |

1095 | 13. The time taken by the block to move from A to B is | 11 |

1096 | Billy jogs ( 2.5 k m ) east in 45 minutes, takes a water break for 12 minutes, and then walks west at a rate of ( 0.65 k m / h ) for 30 min. What is Billy’s average velocity? (Answer units: km/hr) A . 1.52 B. 1.96 ( c cdot 2 ) D. 1.45 | 11 |

1097 | Which physical quantities remain constant in U.C.M? | 11 |

1098 | 31. The maximum range of a projectile is 500 m. If the particle is thrown up a plane, which is inclined at an angle of 30° with the same speed, the distance covered by it along the inclined plane will be a. 250 m b. 500 m c. 750 m d. 1000 m connamundant: no chain | 11 |

1099 | A car travelling at ( 60 mathrm{km} / mathrm{h} ) overtake another car traveling at ( 42 mathrm{km} / mathrm{h} ) Assuming each car to be ( 5.0 m ) long, find the time taken during the overtaking and the total road distance used for the overtake. | 11 |

1100 | – U+al, When a is constant 20. Forces X, Y, and Z have magnitudes 10 N 5 and 5(13+1) N, respectively. The to the same direction as shown in Fig. 3.73. The te of X and Y and the resultant of X and Z have magnitude. Find 0, the angle between X and I. nd Z h | 11 |

1101 | At the uppermost point of a projectile its velocity and acceleration are at an angle of :- A ( cdot 180^{circ} ) B. ( 90^{circ} ) ( c cdot 60^{circ} ) D. ( 45^{circ} ) | 11 |

1102 | A ball is dropped from a great height and the velocity of the ball as a function of time is given ( boldsymbol{v}=frac{boldsymbol{m} boldsymbol{g}}{boldsymbol{K}}left(boldsymbol{1}-boldsymbol{e}^{-(boldsymbol{K} / boldsymbol{m}) t}right) ) where ( m ) is mass of ball, ( K ) is a constant and ( g ) is the acceleration due to gravity. Then, at a time when ( t gg ) ( (boldsymbol{m} / boldsymbol{K}), ) the velocity of the ball becomes A. ( v=g t ) в. ( _{v}=frac{m g}{K} ) c. ( v=frac{m g}{K} ) D. ( v=0 ) | 11 |

1103 | A shell is fired from point 0 on the level ground with velocity ( 50 m / s ) at angle ( 53^{circ} . A ) hill of uniform slope ( 37^{circ} ) starts from point ( A ) that is ( 100 m ) away from the point 0 as shown in the figure. Calculate the time of flight (in seconds) | 11 |

1104 | A projectile is thrown in the upward direction making an angle of 60 with the horizontal direction with a velocity of 47 Then the time after which its inclination with the horizontal is 45 | 11 |

1105 | If the system is in equilibrium ( left(cos 53^{0}=right. ) ( mathbf{3} / mathbf{5}), ) then the value of ( ^{prime} boldsymbol{P}^{prime} ) is ( mathbf{A} cdot 16 N ) B. ( 4 N ) ( mathbf{c} cdot sqrt{208} N ) D. ( sqrt{232} N ) | 11 |

1106 | What is the distance travelled by a point during the time t. if it moves in ( x ) Y plane according to relation. [ begin{array}{l} boldsymbol{X}=boldsymbol{a} boldsymbol{s} boldsymbol{i} boldsymbol{n} boldsymbol{omega} boldsymbol{t} \ boldsymbol{Y}=boldsymbol{a}(1-boldsymbol{c o s} boldsymbol{omega} boldsymbol{t}) end{array} ] | 11 |

1107 | 19. A particle has an initial velocity of 3i +4j and an acceleration of 0.4 +0.3j. Find speed after 10 s. (Hint: v =ū+ āt, when ã is constant] | 11 |

1108 | If ( vec{a}+vec{b}+vec{c}=0,|vec{a}|=3,|vec{b}|=5,|vec{c}|=7 ) then the angle between ( vec{a} & vec{b} ) is? A ( cdot frac{pi}{6} ) в. ( frac{2 pi}{3} ) ( c cdot frac{5 pi}{3} ) D. | 11 |

1109 | 1. A train is moving along a straight line with a constant acceleration a. A boy standing in the train throws a bal forward with a speed of 10 ms, at an angle of 60° to the horizontal. The body has to move forward by 1.15 m inside the train to catch the ball back to the initial height. The acceleration of the train, in ms, is (IIT JEE, 2011) | 11 |

1110 | If the magnitude of the cross product of two vector is ( sqrt{3} ) times to the magnitude of their scalar product the angle between two vector will be : ( A ) B. c. D. | 11 |

1111 | A man throws a packet from a tower directly aiming at his friend who is standing at a certain distance from the base which is same as a height of the tower. If packet is thrown with a speed of ( 4 m / s ) and it hits the ground midway between the tower base ( & ) his friend. Find the height of the tower. (Take ( g= ) ( 9.8 m / s^{2} ) A. 3.8 в. 4.4 ( c .3 .2 ) D. 2.2 | 11 |

1112 | 70. A body is projected with velocity v, from the point A as shown in Fig. 5.203. At the same AV2 time, another body is projected 30) vertically upwards from B with velocity V2. The point B lies vertically below the highest point of first particle. For both the bodies to collide, valv, should be a. 2 b. c. 0.5 d. 1 Fig.5.203 | 11 |

1113 | A cyclist moves in such a way that he takes ( 72^{circ} ) turn towards left after travelling ( 200 mathrm{m} ) in straight line. What is the displacement when he takes just takes fourth turn? A. zero B. 600 ( m ) c. ( 400 mathrm{m} ) D. 200 ( mathrm{m} ) | 11 |

1114 | Speed ( v ) of a particle moving along a straight line, when it is at a distance ( x ) from a fixed point on the line is given by ( v^{2}=108-9 x^{2} ) (assuming mean position to have zero phase constant) (all quantities in are in ( c g s ) unit): A. The motion is uniformly accelerated along the straight line B. The magnitude of the acceleration at a distance ( 3 mathrm{cm} ) from the fixed point is ( 27 mathrm{cm} / mathrm{s}^{2} ) C. The motion is simple harmonic about ( x=sqrt{12} mathrm{m} ) D. The maximum displacement from the fixed point is ( 4 mathrm{cm} ) | 11 |

1115 | 4. Rain is falling vertically with a velocity of 25 ms. woman rides a bicycle with a speed of 10 ms in the north to south direction. What is the direction (angle with vertical) in which she should hold her umbrella to safe herself from rain? a. tan-‘(0.4) b. tan- (1) c. tan-(13) d. tan-(2.6) mouing on a highway with a speed of | 11 |

1116 | A man wearing a wingsuit glides through the air with a constant velocity of ( 47 m s^{-1} ) at an angle of ( 24^{circ} ) to the horizontal. The path of the man is shown n Fig The total mass of the man and the wingsuit is 85 kg. The man takes a time of 2.8 minutes to glide from point ( A ) to point ( boldsymbol{B} ) The pressure of the still air at ( A ) is ( 63 k P a ) and at ( B ) is ( 92 k P a . ) Assume the density of the air in constant between ( boldsymbol{A} ) and ( B ) Determine the density of the air between ( A ) and ( B ) density ( = ) | 11 |

1117 | (110Biciul Cun). 5. Statement I: A body with constant acceleration always moves along a straight line. Statement II: A body with constant magnitude of acceleration may not speed up. | 11 |

1118 | 33. The speed of a projectile at its highest point is v, and at nen the point half the maximum height is v2. If find the angle of projection. a. 45° b. 30° c . 37° d. 60° 12V5′ | 11 |

1119 | Two particles ( A ) and ( B ) are projected with same speed so that ratio of their maximum heights reached is ( 3: 1 . ) If the speed of ( A ) is doubled without altering other parameters, the ratio of horizontal ranges attained by A and B is? | 11 |

1120 | Equation of trajectory of a projectile is given by ( y=-x^{2}+10 x ) where ( x ) and ( y ) are in meters and ( x ) is along horizontal and y is vertically upward and particle is projected from origin. Then which of the following options is/are correct. ( left(g=10 m / s^{2}right) ) A. Initial velocity of particle is ( sqrt{505} mathrm{m} / mathrm{s} ) B. Horizontal range is ( 10 mathrm{m} ) c. Maximum height is 25 m D. Angle of projection with horizontal is ( tan ^{-1}(5) ) | 11 |

1121 | A man projects a coin upwards from the gate of a uniform moving train. The path of coin for the man will be | 11 |

1122 | In uniform circular motion A. acceleration is variable. B. acceleration is uniform. C. the direction and magnitude of acceleration both vary. D. if force applied is doubled in circular motion, then angular velocity becomes double. | 11 |

1123 | is at a height equal 17. The velocity of the projectile when it is at a height to half of the maximum height is sin²e a. v/cos + b. √2 v cose c. √2vsine d. v tan 8 sec | 11 |

1124 | A farmer has to go ( 500 m ) due north, ( 400 m ) due east and ( 200 m ) due south to reach his field. If he takes 20 minutes to reach the field. What is the average velocity of farmer during the walk? A. ( 25 m / min ) в. ( 50 m / min ) c. ( 55 m / min ) D. ( 110 mathrm{m} / mathrm{min} ) | 11 |

1125 | 2. Statement I: The time of flight of a body becomes n times the original value if its speed is made n times. Statement II: This due to the range of the projectile which becomes n times. | 11 |

1126 | A car moving along a circular path of radius R with uniform speed covers an angle ( theta ) during a given time t. What is its average velocity? A ( cdot frac{2 R sin (theta / 2)}{t} ) B. ( frac{2 R cos (theta / 2)}{t} ) c. ( frac{2 R sin (theta)}{t} ) D. ( frac{R sin (theta / 2)}{t} ) | 11 |

1127 | A small sphere of mass ( boldsymbol{m}=mathbf{1} boldsymbol{k} boldsymbol{g} ) is moving with a velocity ( (4 hat{i}-hat{j}) m / s . ) It hits fixed smooth wall and rebounds with velocity ( (hat{mathbf{i}}+mathbf{3} hat{mathbf{j}}) boldsymbol{m} / boldsymbol{s} . ) The coefficient of restitution between the sphere and the wall is ( n / 16 . ) Find the value of ( n ) | 11 |

1128 | Assertion A body with constant acceleration always moves along a straight line. Reason A body with constant acceleration may not speed up. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Reason is correct but assertion is incorrect | 11 |

1129 | A particle moves in a way such that its position can be expressed with ( boldsymbol{x}(boldsymbol{t})= ) ( t^{2}+t-3 ) and with ( y(t)=t^{3}-frac{1}{t-1} ) with being time in seconds. ( x(t) ) and ( boldsymbol{y}(t) ) are both in meters. Initially, how far away is the particle from the origin? A. ( 0.00 m ) в. ( 1.00 m ) c. ( 1.56 m ) D. ( 2.83 m ) E. ( 3.16 m ) | 11 |

1130 | What remains constant in uniform circular motion? A. Velocity B. Speedd c. Displacement D. Direction | 11 |

1131 | If ( vec{a} ) and ( vec{b} ) are two vectors then the value of ( (vec{a}+vec{b}) times(vec{a}-vec{b}) ) is: A ( cdot 2(vec{b} times vec{a}) ) B. ( -2(vec{b} times vec{a}) ) c. ( vec{b} times vec{a} ) D. ( vec{a} times vec{b} ) | 11 |

1132 | • Find the drift of the boat when it is in the middle of the river. 1/3 71/3 b. u +1 d. None of these | 11 |

1133 | A man wearing a wingsuit glides through the air with a constant velocity of ( 47 m s^{-1} ) at an angle of ( 24^{circ} ) to the horizontal. The path of the man is shown n Fig. The total mass of the man and the wingsuit is 85 kg. The man takes a time of 2.8 minutes to glide from point ( A ) to point ( boldsymbol{B} ) Show that the difference in height ( h ) | 11 |

1134 | 4. The trajecto The trajectories of the motion of three particles are shown A 40. Match the entries of Column I with the entries of Column II. VA Fig. A.40 Column I Column II i Time of flight is least for a. ii. Vertical component of the b. velocity is greatest for i. Horizontal component of the velocity is greatest for liv. Launch speed is least for d. No appropriate match given 5 The nath of nroiectile is represented by y = Px – Ox?. | 11 |

1135 | A man rows upstream a distance of ( 9 k m ) or downstream a distance of ( 18 k m ) taking 3 hours each time. The speed of the boat in still water is A ( cdot 7 frac{1}{2} k m / h ) В ( cdot 6 frac{1}{2} k m / h ) c. ( _{5} frac{1}{2} k m / h ) D. ( 4 frac{1}{2} k m / h ) | 11 |

1136 | If ( overline{boldsymbol{A}}=mathbf{2} hat{mathbf{i}}+mathbf{3} hat{boldsymbol{j}}-hat{boldsymbol{k}} ) and ( overline{boldsymbol{B}}=-hat{boldsymbol{i}}+mathbf{3} hat{boldsymbol{j}}+ ) ( 4 hat{k}, ) then projection of ( bar{A} ) on ( bar{B} ) will be: A ( cdot frac{3}{sqrt{13}} ) в. ( frac{3}{sqrt{26}} ) c. ( sqrt{frac{3}{26}} ) D. ( sqrt{frac{3}{13}} ) | 11 |

1137 | w 50. A man is riding on a horse. He is trying to jump the gap between two symmetrical ramps of snow separated by a distance W as shown in Fig. A.26. He launches off the first ramp with a Fig. A.26 speed V. The man and the horse have a total mass m. and their size is small as compared to W The value of initial launch speed V, which will put the horse exactly at the peak of the second ramp is – Wg Wg ** Vsin o x cose V sin(0/2)* cos(0/2) 1 2Wg C. V2 sin cos 0 sin cos e b. Wg | 11 |

1138 | Two locomotives approach each other on the parallel tracks. Each has speed of ( 95 k m / h ) with respect to the ground. If they are initially ( 8.5 k m ) apart, how long will it be before they reach each other? (in hours) ( mathbf{A} cdot 0.045 ) B. 0.065 c. 0.025 D. 0.078 | 11 |

1139 | A thin circular ring of mass ( mathrm{M} ) and radius R is rotating about its axis with a constant angular velocity ( omega . ) Two objects, each of mass ( mathrm{m}, ) are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity: A. ( frac{M omega}{(M+m)} ) в. ( frac{omega(M-2 m)}{(M+2 m)} ) c. ( frac{M omega}{M+2 m} ) D. ( frac{omega(M+2 m)}{M} ) | 11 |

1140 | A particle moves in such a manner that ( boldsymbol{x}=boldsymbol{A t}, boldsymbol{y}=boldsymbol{B} boldsymbol{t}^{3}-boldsymbol{2 t}, boldsymbol{z}=boldsymbol{c} boldsymbol{t}^{2}-boldsymbol{4} boldsymbol{t} ) where ( x, y ) and ( z ) are measured in metres and ( t ) is measured in seconds, and ( A, B ) and ( C ) are unknown constants. Given that the velocity of the particle at ( boldsymbol{t}=2 boldsymbol{s} ) is ( overrightarrow{boldsymbol{v}}=left(frac{boldsymbol{d} overrightarrow{boldsymbol{r}}}{boldsymbol{d} boldsymbol{t}}right)=boldsymbol{3} hat{boldsymbol{i}}+2 boldsymbol{2} hat{boldsymbol{j}} boldsymbol{m} / boldsymbol{s} ) determine the velocity of the particle at ( boldsymbol{t}=mathbf{4} boldsymbol{s} ) ( mathbf{A} cdot 8 hat{i}+94 hat{j}+4 hat{k} m / s ) B. ( 6 hat{i}+94 hat{j}+6 hat{k} m / s ) ( mathbf{c} cdot 3 hat{i}+94 hat{j}+4 hat{k} m / s ) D ( .3 hat{i}+92 hat{j}+4 hat{k} m / s ) | 11 |

1141 | 15. The horizontal distance x travelled by the block in moving from A to C is a. (1+13) b. (1 – 13)m c. (13 + 3)m d. g meter | 11 |

1142 | U O VJ 1115 A projectile can have same range R for two angles of projection. It t, and t2 are the times of flight in the two cases, then what is the product of two times of flight? a. tytz & R² b. tt2 «R c. tit oc al d. tt . – | 11 |

1143 | usuvuvi wauns. 30. During the motion the magnitude of velocity of ram with respect to Shyam is a. 1 ms b. 4 ms- c. 5 ms 1 d. 7 ms! | 11 |

1144 | The minimum number of vectors of unequal magnitude required to produce a zero resultant is : A .2 B. 3 ( c cdot 4 ) D. more than 4 | 11 |

1145 | A man wearing a wingsuit glides through the air with a constant velocity of ( 47 ~ m s^{-1} ) at an angle of ( 24^{circ} ) to the horizontal. The path of the man is shown in Fig. The total mass of the man and the wingsuit is 85 kg. The man takes a time of 2.8 minutes to glide from point ( A ) to point ( boldsymbol{B} ) For the movement of the man from ( A ) to | 11 |

1146 | A stone projected at an angle ( theta ) with horizontal from the roof of a tall building falls on the ground after three seconds. Two seconds after the projection it was again at the level of projection. Then the height of the building is: A . ( 15 mathrm{m} ) в. ( 5 m ) ( c .25 m ) D. ( 20 m ) | 11 |

1147 | The relation between the acceleration and time for an object is given below. Calculate the velocity with which the object is moving at ( boldsymbol{t}=mathbf{1}(mathbf{A t} boldsymbol{t}=mathbf{0}, boldsymbol{v}= ) ( mathbf{0} ) ( boldsymbol{a}=boldsymbol{3} boldsymbol{t}-boldsymbol{4} boldsymbol{t}^{2} ) | 11 |

1148 | The roadway bridge over a canal is in the form of an arc of a circle of radius ( 20 m . ) What is the maximum speed with which a car can cross the bridge without leaving the ground at the highest point. A ( cdot 10 mathrm{ms}^{-1} ) B. ( 12 mathrm{ms}^{-1} ) ( mathrm{c} cdot 14 mathrm{ms}^{-1} ) D. ( 16 mathrm{ms}^{-1} ) | 11 |

1149 | Fill in the blank. In uniform circular motion remains constant. A. Acceleration B. Time c. speed D. Direction | 11 |

1150 | If ( |boldsymbol{v}|= ) const; circular motion place then A ( cdot alpha= ) angular accl” ( = ) const B ( cdot a_{t}= ) const ( mathbf{c} cdot a_{c}= )const D. All are false | 11 |

1151 | 12. An object may have a. varying speed without having varying velocity. b. varying velocity without having varying speed. c. non-zero acceleration without having varvin velocity. d. non-zero acceleration without having varying speed | 11 |

1152 | The minimum number of vectors having different planes which can be added to give zero resultant is A .2 B. 3 ( c cdot 4 ) D. 5 | 11 |

1153 | Let ( vec{a} ) and ( vec{b} ) be unit vectors inclined at an variable angle ( boldsymbol{theta}left(boldsymbol{theta epsilon}left(mathbf{0}, frac{pi}{2}right)left(frac{pi}{2}, boldsymbol{pi}right)right) ) ( operatorname{Let} g(theta)=int_{-(vec{alpha} . vec{b})^{2}}^{-lambda} f^{2}(x) d x+ ) ( int_{lambda}^{|vec{a} times vec{b}|^{2}} f^{2}(x) d x-frac{2}{lambda}, w h e r e lambda>0, ) is function satisfying ( boldsymbol{f}(boldsymbol{x})+boldsymbol{f}(boldsymbol{y})= ) ( frac{boldsymbol{x}+boldsymbol{y}}{boldsymbol{x} boldsymbol{y}}, boldsymbol{x}, boldsymbol{y} epsilon boldsymbol{R}-[mathbf{0}] boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{h}(boldsymbol{theta})= ) ( -g(theta)+|vec{a} times vec{b}|^{2} cdotleft(vec{a} cdot vec{b}_{1}right)^{2}, vec{b}_{1}=2 vec{b} ) ( mathbf{f}|boldsymbol{g}(boldsymbol{theta})| ) is attaining its minimum value, then minimum distance between origin and the point of intersection of lines ( vec{r} times vec{a}=vec{a} times vec{b} ) and ( vec{r} times vec{b}=vec{b} times vec{a} ) is A. ( sqrt{2-sqrt{2}} ) в. ( sqrt{2+sqrt{2}} ) c. ( sqrt{sqrt{2}+1} ) D. ( sqrt{sqrt{2}-1} ) | 11 |

1154 | Which force is required to maintain a body in uniform circular motion? | 11 |

1155 | 17. The direction (angle) with horizontal at which В will appear to move as seen from A is a. 37° b. 53° c. 15° d. 90° | 11 |

1156 | A river ( 400 m ) wide is flowing at a rate of ( 2.0 m / s . A ) boat is sailing at a velocity of ( 10 m / s ) with respect to the water, in a direction perpendicular to the river. ( (boldsymbol{a}) ) Find the time taken by the boat to reach the opposite bank. (b) How far from the point directly opposite to the starting point does the boat reach the opposite bank? | 11 |

1157 | Passengers in the jet transport ( boldsymbol{A} ) flying east at a speed of ( 800 k m / h ) observe a second jet plane ( B ) that passes under the transport in horizontal flight Although the nose of ( B ) is pointed in the | 11 |

1158 | A man wearing a wingsuit glides through the air with a constant velocity of ( 47 m s^{-1} ) at an angle of ( 24^{circ} ) to the horizontal. The path of the man is shown in Fig. The total mass of the man and the wingsuit is ( 85 k g . ) The man takes a time of 2.8 minutes to glide from point ( A ) to point ( boldsymbol{B} ) For the movement of the man from ( A ) to | 11 |

1159 | A motor car is traveling at ( 30 m s^{-1} ) on a circular road of radius ( 500 mathrm{m} ). It is increasing speed at the rate of ( 2 m s^{-2} ) The acceleration of car is : A ( .2 m s^{-2} ) В. 2.7 ( m s^{-2} ) ( c cdot 3 m s^{-2} ) D. 3.7 ( m s^{-2} ) | 11 |

1160 | 18. What is the angle of projectile with the vertical if velocity at the highest point is V2/5 times the velo when it is at a height equal to half of the maxim height? a. 150 b. 30° c. 450 d. 60° | 11 |

1161 | Find the change in velocity of the tip of the minute hand (radius ( =10 mathrm{cm} ) ) of a clock in 45 minutes. ( (text { in } mathrm{cm} / mathrm{min}) ) A ( cdot frac{sqrt{2}}{3} ) B. ( pi frac{sqrt{2}}{2} ) c. ( pi frac{sqrt{3}}{3} ) D. ( pi frac{2}{3} ) | 11 |

1162 | Two particles ( A ) and ( B ) start simultaneously from the same point and move in a horizontal plane. ( A ) has an initial velocity ( u_{1} ) due east and acceleration ( a_{1} ) due north. ( B ) has an initial velocity ( u_{2} ) due north and acceleration ( a_{2} ) due east. Which of the following statements is(are) correct? This question has multiple correct options A. Their paths must intersect at some point B. They must collide at some point. C. They will collide only if ( a_{1} u_{1}=a_{2} u_{2} ) D. If ( u_{1}>u_{2} ) and ( a_{1}<a_{2} ), the particles will have the same speed at some point of time. | 11 |

1163 | A smooth block loosely fits in a circular tube placed on a horizontal surface. The block moves in a uniform circular motion along the tube. Which wall (inner or outer) will exert a non-zero normal contact force on the block? | 11 |

1164 | Enter 1 if true else 0 ( frac{1}{sqrt{3}}(hat{i}+hat{j}+hat{k}) ) is the unit vector in the direction of vector ( overrightarrow{P Q} ) where ( P ) and ( Q ) are the point (1,2,3) and (4,5,6) | 11 |

1165 | Vectors ( vec{a} ) and ( vec{b} ) make an angle ( theta=frac{2 pi}{3} ) If ( |vec{a}|=1,|vec{b}|=2 ) then ( {(vec{a}+3 vec{b}) times(3 vec{a}-vec{b})}^{2}= ) A . 225 B. 250 c. 275 D. 300 | 11 |

1166 | The displacement of a particle is given by ( sqrt{x}=t+1 . ) Which of the following statements about its velocity is true? A. It is zero B. It is constant but not zer c. It increases with time D. It decreases with time | 11 |

1167 | Two forces are such that the sum of their magnitude is ( 18 N ) and their resultant is ( 12 N ) and it is also perpendicular to the smaller force.Then the magnitude of the forces are A ( .12 N, 6 N ) B . ( 13 N, 5 N ) c. ( 10 N, 8 N ) D. ( 16 N, 2 N ) | 11 |

1168 | A particle ( P ) is sliding down a frictionless hemispherical bowl. It passes the point ( A ) at ( t=0 . ) At this instant of time, the horizontal component of its velocity is ( v . A ) bead ( Q ) of the same mass as ( P ) is ejected from ( A ) at ( t=0 ) along the horizontal string ( A B, ) with the speed ( v . ) Friction between the bead and the string may be neglected. Let ( t_{p} ) and ( t_{q} ) be the respective times taken by ( P ) and ( Q ) to reach the point ( boldsymbol{B} ). Then ( mathbf{A} cdot t_{p}t_{q} ) D. ( _{t_{p} / t_{q}}=frac{text {length of are } A C D}{text {length of cord } A B} ) | 11 |

1169 | The direction cosines of ( hat{i}+hat{j}+hat{k} ) are ( mathbf{A} cdot 1,1,1 ) B. 2,2,2 c. ( 1 / sqrt{2}, 1 / sqrt{2}, 1 / sqrt{2} ) D. ( 1 / sqrt{3}, 1 / sqrt{3}, 1 / sqrt{3} ) | 11 |

1170 | Fill in the blank. In circular motion, force is always to the displacement. A. Perpendicular B. Parallel c. opposite D. None | 11 |

1171 | Which of the following represent circular motion A. Ball sliding down an inclined plane B. Motion of a simple pendulum c. A freely falling body D. A stone tied to a thread and whirled | 11 |

1172 | 5. 100 coplanar forces each equal to 10 N act on a body. Each force makes angle tu/50 with the preceding force. What is the resultant of the forces (a) 1000 N (b) 500 N (c) 250 N (d) Zero | 11 |

1173 | 2. A projectile fired from the ground follows a parabolic path. The speed of the projectile is minimum at the top of its path (UIT JEE, 1984) | 11 |

1174 | In the projectile motion, if air resistance is ignored, the horizontal motion is at A. constant acceleration B. variable acceleration C. constant velocity D. constant retardation | 11 |

1175 | fu) v3 9. Maximum and minimum magnitudes of the resultant of two vectors of magnitudes P and Q are in the ratio 3:1. Which of the following relations is true? (a) P=2Q (b) P=Q (c) PQ = 1 (d) None of these | 11 |

1176 | 4. A golfer standing on level ground hits a ball with a velocity of 52 ms at an angle above the horizontal. tan O= 5/12, then find the time for which the ball is atleast 15 m above the ground (take g = 10 ms). at an angle of A to | 11 |

1177 | Rain is falling vertically with ( 3 m s^{-1} ) and a man is moving due North with ( 4 m s^{-1} . ) In which direction he should hold the umbrella to protect himself from rains? A ( cdot 37^{circ} ) North of vertical B. ( 37^{circ} ) South of vertical C. ( 53^{circ} ) North of vertical D. ( 53^{circ} ) South of vertical | 11 |

1178 | In circular motion, the A. Direction of motion is fixed B. Direction of motion changes continuously C. Acceleration is zero D. Velocity is constant | 11 |

1179 | A projectile is thrown in the upward direction making an angle of ( 60^{circ} ) with the horizontal direction with a velocity of ( 147 m s^{-1} . ) Then the time after which its inclination with the horizontal is ( 45^{circ} ) is (Take ( boldsymbol{g}=mathbf{9 . 8} boldsymbol{m} / boldsymbol{s}^{2} ) ) A . ( 15 s ) B. ( 10.98 s ) c. ( 5.49 s ) D. 2.745 ( s ) | 11 |

1180 | The two adjacent sides ( boldsymbol{O A}, boldsymbol{O B} ) of parallelogram are ( 2 hat{i}+4 hat{j}-5 hat{k} ) and ( hat{i}+ ) ( 2 hat{j}+3 hat{k} . ) The unit vectors along the diagonals of the parallelogram are given by A ( cdot frac{(3 hat{i}+6 hat{j}-2 hat{k})}{7} ) B. ( frac{(-hat{i}-2 hat{j}+8 hat{k})}{sqrt{69}} ) ( frac{(-3 hat{i}-6 hat{j}+2 hat{k})}{7} ) D. ( frac{(hat{i}+2 hat{j}-8 hat{k})}{sqrt{69}} ) | 11 |

1181 | A man walks 12 steps in Northern direction and turns left to walk 5 steps, then returns to the initial point by the shortest path. Find the distance travelled given each step is ( 0.3 mathrm{m} ) A . ( 5.1 mathrm{m} ) B. ( 9 mathrm{m} ) ( c cdot o m ) D. 3.6 m | 11 |

1182 | Illustration 5.71 A fan is rotating with angular velocity 100 revs-‘. Then it is switched off. It takes 5 min to stop. a. Find the total number of revolution made before the fan stops. (assume uniform angular retardation). b. Find the value of angular retardation. c. Find the average angular velocity during this interval. | 11 |

1183 | Two particles are projected under gravity with speed ( 4 mathrm{m} / mathrm{s} ) and ( 3 mathrm{m} / mathrm{s} ) simultaneously from same point and at angles ( 53^{circ} ) and ( 37^{circ} ) with the horizontal surface respectively as shown in figure. Then: This question has multiple correct options A. Their relative velocity is along vertical direction. B. Their relative acceleration is non-zero and it is along vertical direction. C. They will hit the surface simultaneously D. Their relative velocity is constant and has magnitude ( 1.4 mathrm{m} / mathrm{s} ) | 11 |

1184 | A river is flowing from west to east at a speed of ( 5 mathrm{m} / mathrm{min}^{-1} ). A man on the south bank of the river, capable of swimming at ( 10 m / m i n^{-1} ) in still waters wants to swim the river in the shortest time. In which direction should swim in a direction A ( .30^{circ} ) west of north B. ( 60^{circ} ) east of north ( mathbf{c} cdot 30^{circ} ) east of north D. due north | 11 |

1185 | A man of mass ( 62 mathrm{kg} ) is standing on a stationary boat of mass 238 kg. The man is carrying a sphere of mass ( 0.5 mathrm{kg} ) in his hands. If the man throws the sphere horizontally with a velocity of ( 12 m s-1, ) find the velocity with which the boat will move (in magnitude) A ( .0 .02 m s^{-1} ) B. ( 0.5 m s^{-1} ) C. ( 0.04 m s^{-1} ) D. ( 0.06 m s^{-1} ) | 11 |

1186 | At what angle should a body be projected with a velocity ( 24 frac{m}{s} ) just to pass over the obstacle ( 14 mathrm{m} ) high of a distance of ( left.24 m . text { (Take } g=10 m / s^{2}right) ) ( mathbf{A} cdot tan theta=3.8 ) B. ( tan theta=1 ) ( mathbf{c} cdot tan theta=3.2 ) D. ( tan theta=2 ) | 11 |

1187 | Two towns ( T_{1} ) and ( T_{2} ) are connected by a regular bus service. A scooterist moving from ( boldsymbol{T}_{1} ) to ( boldsymbol{T}_{2} ) with speed of ( 20 k m h^{-1} ) notices that a bus goes past it every 21 minutes in the direction of his motion and every 7 minutes in the opposite direction. If a bus leaves in either direction every ( t ) minutes, the period ( t ) is A . 1.5 minute B. 9.5 minute c. 6 minute D. 10.5 minute | 11 |

1188 | When a particle moves in a circle with a uniform speed A. its velocity and acceleration are both constant B. its velocity is constant but the acceleration changes C. its acceleration is constant but the velocity changes D. its velocity and acceleration both change | 11 |

1189 | The distance covered by a particle in ( t ) second is given by ( boldsymbol{x}=mathbf{3}+mathbf{8} boldsymbol{t}-mathbf{4} boldsymbol{t}^{2} ) After ( 1 s ) its velocity will be A. 0 unit ( / ) s B. 3unit/ c. ( 4 u n i t / s ) D. ( 7 u n i t / s ) | 11 |

1190 | A particle of mass ( mathrm{m} ) is tied to a string of length L. The free end of the string is fixed and the particle is whirled in a circular path. The speed of the particle increases from ( 5 mathrm{m} / mathrm{s} ) to ( 10 mathrm{m} / mathrm{s} ) for 5 secs. The motion is A. Uniform circular motion B. Non-uniform circular motion c. Non uniformly accelerated motion D. Non of these | 11 |

1191 | A pendulum is suspended from the roof of a rail road car. When the car is moving on a circular track the pendulum inclines. A. Forward B. Rearward c. Towards the centre of the path D. Away from the centre of the path | 11 |

1192 | 3. A policeman moving on a highway with a speed of 30 km h-‘fires a bullet at thief’s car speeding away in the same direction with a speed of 192 kmh. If the muzzle speed of the bullet is 150 ms, with what speed does the bullet hit the thief’s car? a. 120 ms? b. 90 ms -1 c. 125 ms -1 d. 105 ms | 11 |

1193 | A frog sits on the end of a long board of length ( L=10 c m . ) The board rests on frictionless horizontal table. The frog wants to jump to the opposite end of the board. What is minimum take of speed ( v ) in ( m s^{-1} ) relative to the ground that the frog follows to do the tricks? [Assume that the board and frog have equal masses?] A ( cdot 2 sqrt{5} m s^{-1} ) B. ( 5 m s^{-1} ) D. ( 10 sqrt{2} mathrm{ms}^{-1} ) | 11 |

1194 | 16. The angle o which the velocity vector of stone makes wi horizontal just before hitting the ground is given by: (a) tan o = 2 tane (b) tan o = 2 cot 0 (c) tan $ = V2 tan 0 (d) tan º = 12 cos 0 | 11 |

1195 | If a line makes angles ( 90^{0}, 135^{0}, 45^{0} ) with ( X, Y ) and ( Z ) axes respectively, then find its direction cosines. | 11 |

1196 | The direction of which of the following vectors is along the line of axis of rotation? A. Angular velocity, angular acceleration only B. Angular velocity, angular momenturm only c. Angular velocity, angular acceleration, angular momentum only D. Angular velocity, angular acceleration, angular momentum and torque | 11 |

1197 | A particle is projected at an angle ( boldsymbol{theta}= ) ( 30^{circ} ) with the horizontal, with a velocity of ( 10 m s^{-1} . ) Then This question has multiple correct options A. After ( 2 s ), the velocity of particle makes an angle of ( 60^{circ} ) with initial velocity vector. B. After ( 1 s ), the velocity of particle makes an angle of ( 60^{circ} ) with initial velocity vector c. The magnitude of velocity of particle after 1 s is ( 10 mathrm{ms}^{-1} ) D. The magnitude of velocity of particle after 1 s is ( 5 m s^{-1} ) | 11 |

1198 | A police van moving on a highway with a speed of ( 30 mathrm{km} / mathrm{hr} ) fires a bullet at a thief’s car speeding away in the same direction with a speed of ( 192 k m / h r ) If the muzzle speed of the bullet is ( 150 m / s, ) with what speed does the bullet hit the thief’s car? (Note:Obtain that speed which is relevant for damaging the thief’s car) | 11 |

1199 | 36. The vector sum of two forces is perpendicular to their vector difference. The forces are a. Equal to each other b. Equal to each other in magnitude C. Not equal to each other in magnitude d. Cannot be predicted 37 If none111 | 11 |

1200 | A gramophone disc is rotating at 78 rotations per minute. Due to power cut, it comes to rest after ( 30 s ). The angular retardation of the disc will be : A. 0.27 radians ( / sec ^{2} ) B. 0.127 radians ( / ) sec ( ^{2} ) c. 12.7 radians ( / mathrm{secc}^{2} ) D. zero. | 11 |

1201 | The resultant of ( vec{A} times overrightarrow{0} ) will be equal to: A . zero в. ( A ) c. zero vector D. unit vector | 11 |

1202 | 23. A particle has been projected with a speed of 20 ms at an angle of 30° with the horizontal. The time taken when the velocity vector becomes perpendicular to the initial velocity vector is a. 4s b. 2 s c. 3s d. Not possible in this case | 11 |

1203 | SULVEW LAAIPLES Example 5.1 Two towers AB and CD are situated at distance d apart as shown in Fig. 5.168. AB is 20 m high and CD is 30 m high from the ground. An obiect of mass m is thrown from the top of AB horizontally with a velocity of 10 ms towards CD. Simultaneously, another object of mass amis thrown from the top of CD at an angle 60° to the horizontal towards AB with the same magnitude of initial velocity as that of the first object. The two objects move in the same vertical plane, collide in mid-air, and stick to each other. 30 m 20 m Fig. 5.168 a. Calculate the distance d between the towers. b. Find the position where the objects hit the ground. | 11 |

1204 | o alue Lal ! (cs) 7. A staircase contains three steps staircase contains three steps each 10 cm high and 20 cm wide. What should be the minimum hori- zontal velocity of the ball rolling off the upper- most plane so as to hit directly the lowest plane? (in ms- Fig. 5.210 | 11 |

1205 | A particle is moving with velocity ( vec{v}= ) ( K(y hat{i}+x hat{j}), ) where ( K ) is a constant. The general equation for its path is A ( cdot y^{2}=x^{2}+ ) contant B . ( y=x^{2}+ ) contant C ( cdot y^{2}=x+ ) contant D. ( x y= ) contant | 11 |

1206 | 48. A body is projected horizontally from the top of a tower with initial velocity 18 ms. It hits the ground at angie 45°. What is the vertical component of velocity when strikes the ground? a. 9 ms -1 b. 9/2 ms-1 c. 18 m s-1 d. 18/2 ms-1 | 11 |

1207 | Two particle move in a uniform gravitational field with an acceleration ( g . ) At the initial moment the particles were located over a tower at one point and moved with velocities ( boldsymbol{v}_{1}=mathbf{3} boldsymbol{m} / s ) and ( v_{2}=4 m / s ) horizontally opposite directions. Find the distance between the particles at the moment when their velocity vectors become mutually perpendicular. | 11 |

1208 | 48. Jai is standing on the top of a building of height 25 m he wants to throw his gun to Veeru who stands on top of another building of height 20 m at distance 15 m from first building. For which horizontal speed of projection, it is possible? a. 5 ms b. 10 ms? c. 15 ms 1 d. 20 ms? 101112 | 11 |

1209 | A projectile aimed at a mark which is in the horizontal plane through the point of projection falls a cm short of it when the elevation is ( alpha ) and goes ( b c m ) too far when the elevation is ( beta . ) Show that if the velocity of projection is same in all the case, the proper elevation is ( frac{1}{2} sin ^{-1}left[frac{b sin 2 alpha+a sin 2 beta}{a+b}right] ) | 11 |

1210 | In uniform circular motion the velocity is A. Constant B. Variable ( c cdot>1 ) D. None | 11 |

1211 | A particle moves in a circle of radius 1.0 ( c m ) with a speed given by ( v=2 t ) where ( v ) is in ( c m / s ) and ( t ) in seconds. Find the radial acceleration of the particle at ( t=1 s: ) ( mathbf{A} cdot 2.0 mathrm{cms}^{-2} ) B. ( 3.0 mathrm{cms}^{-2} ) c. ( 4.0 mathrm{cms}^{-2} ) D. ( 5.0 mathrm{cms}^{-2} ) | 11 |

1212 | What happens to the centripetal acceleration of a revolving body if you double the orbital speed ( v ) and half angular velocity ( omega ) A. It remains unchanged B. It is halvedd c. It is doubleo D. It is quadrupled | 11 |

1213 | A ball is thrown at angle ( theta ) and another ball is thrown at an angle ( (90-theta) ) with the horizontal direction from the same point with the same speed ( 40 m s^{-1} ). The second ball reaches ( 50 m ) higher than the first ball. Find their individual heights. A. ( 20 m, 70 m ) B . ( 25 m, 75 m ) ( mathbf{c} cdot 15 m, 65 m ) D. ( 10 m, 60 m ) | 11 |

1214 | A boat takes 2 hours to travel ( 8 k m ) and back in still water lake. With water velocity of ( 4 k m / h, ) the time taken for going upstream of ( 8 k m ) and coming back is A. 160 minutes B. 80 minutes c. 100 minutes D. 120 minutes | 11 |

1215 | Consider two vectors ( vec{A} ) and ( vec{B} ). Let these two vectors represent two adjacent sides of a parallelogram. We construct a parallelogram OACB as shown in the diagram. Which of the following represent the resultant vector? ( A cdot O A ) в. ( O C ) ( c . O B ) D. None | 11 |

1216 | Find the initial velocity of projection of a ball thrown vertically up if the distance moved by it in ( 3^{r d} ) second is twice the distance covered by it in 5th second. (Take ( left.g=10 mathrm{m} s^{-2}right) ) A. ( 85 mathrm{m} s^{-1} ) B. 75 ( mathrm{m} s^{-1} ) c. ( 65 mathrm{m} s^{-1} ) D. ( 95 mathrm{m} s^{-1} ) | 11 |

1217 | For a projectile, the physical quantities which remain constant are: A. vertical component of velocity and kinetic energy B. potential energy and kinetic energy c. acceleration and horizontal component of velocity D. potential energy and acceleration | 11 |

1218 | A body of mass ( 50 mathrm{kg} ) revolves in a circle of diameter ( 0.40 mathrm{m}, ) making 500 revolutions per minute. Calculate linear velocity and centripetal acceleration | 11 |

1219 | 62. Two balls A and balls A and B are thrown with speeds u and u/2, spectively. Both the balls cover the same horizontal Distance before returning to the plane of projection. If the angle of projection of ball B is 15° with the horizontal. then the angle of projection of A is su a. sin -1 | 11 |

1220 | The important characteristic that distinguishes uniform from non uniform circular motion are A. Uniform circular motion has radial acceleration and radial velocity, while non uniform motion lacks it B. Uniform circular motion has radial acceleration and tangential velocity, while non uniform motion lacks it C. Non uniform circular motion has tangential acceleration, while uniform circular motion lacks it D. Non uniform circular motion has tangential acceleration and radial velocity, while uniform circular motion lacks it | 11 |

1221 | A body is projected vertically upwards. The times corresponding to height ( h ) while ascending and while descending are ( t_{1} ) and ( t_{2} ) respectively. Then the velocity of projection is ( (g ) is acceleration due to gravity) A. ( g sqrt{t_{1} t_{2}} ) an ( t_{2} ) в. ( frac{g t_{1} t_{2}}{t_{1}+t_{2}} ) c. ( frac{g sqrt{t_{1} t_{2}}}{2} ) D. ( frac{gleft(t_{1}+t_{2}right)}{2} ) | 11 |

1222 | A stone is dropped into water from a bridge ( 44.1 mathrm{m} ) above the water. Another stone is thrown vertically downward one second later. Both strike the water simultaneously, then the initial speed of the second stone is A ( cdot 12.25 mathrm{ms}^{-1} ) B . ( 14.75 mathrm{ms}^{-1} ) c. ( 16.23 m s^{-1} ) D. ( 17.15 mathrm{ms}^{-1} ) | 11 |

1223 | 32. The time t when they are at shortest distance from each other subsequently, is – a. 8.8 s b. 12 s c. 15 d. 44 s | 11 |

1224 | – V. – Wall (R ) Illustration 5.69 A particle moves in a circular path such that its speed v varies with distance s as v = Vs, where is a positive constant. Find the acceleration of the particle after traversing a distance s. | 11 |

1225 | A car moving with a speed of ( 40 mathrm{km} / mathrm{h} ) can be stopped by applying brakes at least after ( 2 mathrm{m} ). If the same car is moving with a speed of ( 80 mathrm{km} / mathrm{h} ), what is the minimum stopping distance? ( A cdot 8 c m ) B. ( 6 m ) ( c .4 m ) D. ( 2.6 m ) | 11 |

1226 | 15. Rain, driven by the wind, falls on a railway compartment with a velocity of 20 ms, at an angle of 30° to the vertical. The train moves, along the direction of wind flow, at a speed of 108 km h . Determine the apparent velocity of rain for a person sitting in the train. a. 20/7 ms b. 1077 ms -1 c. 1577 ms- t d . 1077 km h — | 11 |

1227 | – – – – – 2. A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is h (a) + 2hg 60 8 | 11 |

1228 | What is rotatory motion? | 11 |

1229 | A body is projected horizontally from the top of a tower with initial velocity ( 18 m s^{-1} . ) It hits the ground at angle ( 45^{circ} ) What is the vertical component of velocity when strikes the ground? B. ( 18 m s^{-1} ) ( mathrm{D} cdot 9 mathrm{ms}^{-1} ) | 11 |

1230 | 27. A projectile has a time of flight T and range R. If the time of flight is doubled, keeping the angle of projection same what happens to the range? a. R/4 b. R/2 c. 2 d. 4R | 11 |

1231 | Figure shows three vectors ( vec{a}, vec{b} ) and ( vec{c} ) where ( R ) is the midpoint of ( P Q ). Then which of the following relations is correct? A. ( vec{a}+vec{b}=2 vec{c} ) в. ( vec{a}+vec{b}=vec{c} ) c. ( vec{a}-vec{b}=2 vec{c} ) D. ( vec{a}-vec{b}=vec{c} ) | 11 |

1232 | shell fired from the ground is just able to cross horizontally the top of a wall 90 m away and 45 m high. The direction of projection of the shell will be 2 250 b. 30° C. 60° do 45°. | 11 |

1233 | Six particles are situated at the corners of a regular hexagon of side ( a ), they move at a constant speed ( v ). Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet each other: A ( cdot 2 ) a/v B. 3 a/v ( c cdot 5 a / v ) D. 6 a/v | 11 |

1234 | When a vector of magnitude 12 units is added to a vector of magnitude 8 units, the magnitude of the resultant vector will be: A. exactly 4 units B. exactly 20 unit c. exactly 2 unitt D. O units, 10 units, or some value between them E. 4 units, 20 units, or some value between them | 11 |

1235 | Circular motion is a example of A. ( 1- ) D motion B. 2-D motion c. 3-D motion D. None | 11 |

1236 | A particle moves with a uniform speed of ( 5 mathrm{m} / mathrm{s} ) in a circular path. If the speed increases to ( 8 mathrm{m} / mathrm{s} ) in the 20 th second The motion of the particle in the 22 nd second will be A. Uniform circular motion B. Non uniform circular motion c. Linear motion, since the particle flies off from the circular path D. Non linear motion, since velocity has increased | 11 |

1237 | 3. A particle at a height ‘h’ from the ground is projected with an angle 30° from the horizontal, it strikes the ground making angle 45° with horizontal. It is again projected from the same point with the same speed but with an angle of 60° with horizontal. Find the angle it makes with the horizontal when it strikes the ground: (a) tan-1 (4) (b) tan-1 (5) (c) tan-1 (15) (d) tan-1 (13) | 11 |

1238 | A ball is projected from level ground with a velocity of ( 40 mathrm{m} / mathrm{s} ) at an angle of ( 30^{circ} ) from the ground. Calculate the vertical component of the projectile’s velocityjust before it strikes the ground? (Take ( left.sin 30^{circ}=0.5, cos 30^{circ}=0.87right) ) ( A cdot 10 mathrm{m} / mathrm{s} ) B. 20 ( mathrm{m} / mathrm{s} ) ( c .30 mathrm{m} / mathrm{s} ) D. 35 m/s E. ( 40 mathrm{m} / mathrm{s} ) | 11 |

1239 | Define following: Position vector | 11 |

1240 | 2. Velocity of a stone projected, 2 second before it reaches the maximum height, makes angle 53° with the horizontal then the velocity at highest point will be (a) 20 m/s (b) 15 m/s (c) 25 m/s (d) 80/3 m/s | 11 |

1241 | 13. A body is projected at angle of 30° and 60° with the same velocity. Their horizontal ranges are R, and R, and maximum heights are H, and H2, respectively, then | 11 |

1242 | Starting from rest, the acceleration of a particle is ( a=2(t-1) . ) The velocity of the particle at ( t=5 s ) is: A. ( 15 mathrm{m} / mathrm{s} ) B. ( 25 mathrm{m} / mathrm{s} ) ( mathbf{c} cdot 5 m / s ) D. None of these | 11 |

1243 | A plane is flying horizontally at ( 98 m s^{-1} ) and releases an object which reaches the ground in ( 10 s . ) The angle made by it while hitting the ground is: A . 55 B . 45 c. 60 D. 75 | 11 |

1244 | Three particles ( A, B ) and ( C ) are situated at the vertices of an equilateral triangle of side ( r ) at ( t=0 . ) The particle ( A ) heads towards ( B, B ) towards ( C, C ) towards ( A ) with constant speeds ( v . ) Find the time of their meeting. | 11 |

1245 | P O5ound. 19. A bomber plane moves due east at 100 kmh over a town T at a certain instant of time. Six minutes later, an interceptor plane sets off flying due north-east from the station S which is 40 km south of T. If both maintain their courses, find the velocity with which the interceptor plane must fly in order to just overtake the bomber. | 11 |

1246 | A particle moves according to the equation ( x=a sin omega t ) and ( y=a(1- ) ( cos omega t) . ) The path of the particle is A . circle B. parabola c. hyperbola D. cycloid E . ellipse | 11 |

1247 | A player kicks a ball at a speed of 20 ( m s^{-1} ) so that its horizontal range is maximum. Another player 24 m away in the direction of kick starts running in the same direction at the same instant of hit. If he has to catch the ball just before it reaches the ground, he should run with a velocity equal to (Take ( g=10 ) ( m s-2) ) A ( cdot 2 sqrt{2} mathrm{ms}^{-1} ) B. ( 4 sqrt{2} mathrm{ms}^{-1} ) ( c cdot 6 sqrt{2} m s^{-1} ) D. ( 10 sqrt{2} mathrm{ms}^{-1} ) | 11 |

1248 | The motion of a body is given by the equation ( frac{d v}{d t}=6-3 v ) where v is the speed in ( m s^{-1} ) and ( t ) is time in s. The body is at rest at ( t=0 . ) The speed varies with time as A ( cdot v=left(1-e^{-3 t}right) ) B . ( v=2left(1-e^{-3 t}right) ) c. ( v=left(1+e^{-2 t}right) ) D ( cdot v=2left(1+e^{-2 t}right) ) | 11 |

1249 | a. 5, 10, 20 37. A particle slides from rest from the topmost po I rest from the topmost point of a ucal circle of radius r along a smooth chord making an angle with the vertical. The time of descent is a. Least for O=0 b. Maximum for O=0 c. Least for 0 = 45º d . Independent of e | 11 |

1250 | Illustration 5.32 An inclined plane makes an angle o = 30 with the horizontal. A particle is projected from this plane with a speed of 5 ms’ at an angle of elevation ß= 30° with the horizontal as shown in Fig. 5.53. 5 ms- Fig. 5.53 a. Find the range of the particle on the plane when it strikes the plane. b. Find the range of the particle for B= 120°. | 11 |

1251 | A particle moving along ( x- ) axis whose position is given by ( boldsymbol{x}=mathbf{4}-mathbf{9} boldsymbol{t}+frac{boldsymbol{t}^{mathbf{3}}}{mathbf{3}} ) then choose the correct statement(s) for this motion- This question has multiple correct options A. Direction of motion is not changing at any of the instants B. For ( 0<t<3 s ), the particle is slowing down c. Direction of motion is changing at ( t=3 )sec D. For ( 0<t<3 s ) the particle is speeding up | 11 |

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