Units And Measurement Questions

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

List of units and measurement Questions

Question No Questions Class
1 Mass of a body is ( 210 mathrm{gm} ) and its density is ( 7.981 g m / c m^{3} . ) What will be its volume with regard to significant digits?
A ( cdot 26.312 mathrm{cm}^{3} )
В. ( 26 mathrm{cm}^{3} )
( mathbf{c} cdot 27 c m^{3} )
D. ( 26.3 c m^{3} )
11
2 14. Density of a liquid in CGS system is 0.625 g/cm². What
is its magnitude in SI system?
(a) 0.625
(b) 0.0625
(c) 0.00625
(d) 625
11
3 The temperatures of two bodies
measured by a thermometer are ( t_{1}= )
( mathbf{2 0}^{o} boldsymbol{C} pm mathbf{0 . 5}^{o} boldsymbol{C} ) and ( boldsymbol{t}_{2}=mathbf{5 0}^{o} boldsymbol{C} pm )
( 0.5^{circ} mathrm{C} . ) The temperature difference and
the error there is
( mathbf{A} cdot 30^{circ} C pm 1^{circ} C )
B ( cdot 70^{circ} mathrm{C} pm 0.5^{circ} mathrm{C} )
( mathbf{c} cdot 30^{circ} C pm 0.5^{circ} mathrm{C} )
D. ( 70^{circ} mathrm{C} pm 1^{circ} mathrm{C} )
11
4 Calculate the mean % error in five
observations:
80.0,80.5,81.0,81.5,82
A . ( 0.75 % )
в. ( 1.74 % )
c. ( 0.38 % )
D. ( 1.38 % )
11
5 A vernier callipers has its main scale of ( 10 mathrm{cm} ) equally divided into 200 equal parts. Its vernier scale of 25 divisions
coincides with ( 12 mathrm{mm} ) on the main
scale. The least count of the instrument
is –
( A cdot 0.020 mathrm{cm} )
B. ( 0.002 mathrm{cm} )
c. ( 0.010 mathrm{cm} )
D. ( 0.001 mathrm{cm} )
11
6 12. A small steel ball of radius r is allowed to fall under
gravity through a column of a viscous liquid of coefficient
of viscosity n. After some time the velocity of the ball
attains a constant value known as terminal velocity Dr. The
terminal velocity depends on (i) the mass of the ball m, (ii)
n, (iii) r and (iv) acceleration due to gravity 8. Which of
the following relations is dimensionally correct?
(b) vra nr
ηr
mg
(c) V« nrmg
(d) vya mgr
11
7 A spherometer has 10 threads per ( mathrm{cm} ) and its circular scale has 50 divisions.
The least count of the instrument is
A . ( 0.01 mathrm{cm} )
B. ( 0.02 mathrm{cm} )
c. ( 0.002 mathrm{cm} )
D. ( 0.2 mathrm{cm} )
11
8 The number of times a standard
quantity is present in a given physical quantity, is called its units
A. True
B. False
c. Ambiguous
D. Data insufficient
11
9 At the surface of a certain planet,
acceleration due to gravity is one quarter of that on earth. A brass ball is
transported to this planet, then find the percentage change in its weight.
A . ( 50 % )
B . 25%
c. ( 75 % ) %
D. 100%
11
10 A light year is unit of
A. acceleration
B. distance
( mathbf{C} cdot ) speed
D. velocity
E . time
11
11 What is the order of magnitude of the distance of a quasar from us if light takes 2.9 billion years to reach us?
A ( cdot 2.7 times 10^{25} mathrm{m} )
В. ( 10^{25} mathrm{m} )
( mathbf{c} cdot 10^{2} 4 m )
D. ( 3 times 10^{25} m )
11
12 The wavelength of light is 589 nm. What is its order of magnitude in metre? 11
13 des
7. A physical parameter a can be determined by measuring
bºcB
the parameters b, c, d and e using the relation a =
If the maximum errors in the measurement of b, c, d and
e are b, %, c, %, d, % and e, %, then the maximum error
in the value of a determined by the experiment is
(a) (b1++d, + e) %
(b) (b, +C1-dı- e,) %
(c) (ab, + Bcı – yd- de)%
(d) (ab, + Bc7 + ydı + de %
11
14 Arrange the following lengths in descending order of their magnitudes:
Light year, parsec end Astronomical unit
11
15 ( mathbf{A} )
is the interval from one
noon to the next noon
A. mean solar day
B. solar day
c. lunar day
D. day
11
16 A student measure the height h of a convex mirror using spherometer. The legs of the spherometer are ( 4 mathrm{cm} ) apart and there are 10 divisions per cm on its linear scale and circular scale has 50
divisions. The student takes 2 as linear
scale division and 40 as circular scale
division. What is the radius of curvature
of the convex mirror?
A. ( 9.06 mathrm{cm} )
в. ( 20.66 mathrm{cm} )
( c .5 .66 mathrm{cm} )
D. ( 9.66 mathrm{cm} )
11
17 To find the convergence factor between the units of same physical quantities in two different system 11
18 The length ( ell, ) breadth b and thickness of a block of wood were measured with
the help of a measuring scale. The results with permissible errors are ( ell= ) ( 15.12 pm 0.01 mathrm{cm}, mathrm{t}=5.28 pm 0.01 mathrm{cm} . b= )
( 10.15 pm 0.01 mathrm{cm} . ) The percentage error in volume upto proper significant figures is :
A . 0.28%
B . 0.36%
c. ( 0.48 % )
D . 0.64%
11
19 The distance covered by a body in time ( (mathbf{5 . 0} pm mathbf{0 . 6}) ) is ( (mathbf{4 0 . 0} pm mathbf{0 . 4}) mathrm{m} . ) Calculate
the speed of the body. Also determine
the percentage error in the speed.
11
20 To determine the Youngs modulus of a wire,the formula is ( boldsymbol{Y}=frac{boldsymbol{F}}{boldsymbol{A}} times frac{boldsymbol{Delta} boldsymbol{L}}{boldsymbol{L}} )
where ( L= ) length, ( A= ) area of cross
section of the wire, ( Delta mathrm{L}= ) change in length of the wire when stretched with a force F. The conversion factor to change
it from CGS to MKS system is :
( A cdot 1 )
B. 10
c. ( 0 . )
D. 0.01
11
21 With due regards to significant figures
( 5.4 times 0.125 ) is equal to:
A. 0.7
B. 0.68
c. 0.667
D. none of these
11
22 If the mass of a body is ( 12.1 mathrm{g} ) and its density is ( 2.2 mathrm{g} / mathrm{cc}, ) its volume is.
( mathbf{A} cdot 5.5 mathrm{cm}^{3} )
B. 8 сс
c. 11 сс
D. 55 сс
11
23 The time taken by the earth to complete one rotation about is own axis is called
A. Solar day
B. Mean solar day
c. 1 hour
D. None
11
24 The radius of the sun is ( 7 times 10^{8} m ) and
its mass is ( 2 times 10^{30} k g ). What is the
order of magnitude of density of the
sun?
( mathbf{A} cdot 1.4 times 10^{3} k g / m^{3} )
В ( cdot 10^{7} k g / m^{3} )
c. ( 1.5 times 10^{3} k g / m^{3} )
D. ( 10^{3} k g / m^{3} )
11
25 The volume of a sphere is ( 1.76 mathrm{cm}^{3} ). The
volume of 25 such spheres according to the idea of significant figures in ( mathrm{cm}^{3} ) is
A . 44.00
B. 44.0
( c cdot 44 )
D. 4.4
11
26 Assertion
A number 2.746 rounded off to three
significant figures is ( 2.75, ) while the number 2.743 would be 2.74
Reason
In rounding off the uncertain digits, the preceding digit is raised by 1 if the insignificant digit to be dropped is more than 5 and is left unchanged if the latter is less than 5
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
27 The number of significant figures in 500.06 is
A .2
B. 3
( c cdot 5 )
D. o
11
28 An equation is given here ( left(boldsymbol{P}+frac{boldsymbol{a}}{boldsymbol{V}^{2}}right)= )
( b frac{9}{V} ) where ( P= ) pressure, ( V= ) Volume
and ( theta= ) Absolute temperature. if ( a ) and ( b )
are constants, the dimension of a will
be
( mathbf{A} cdotleft[M L^{-5} T^{-1}right] )
B ( cdotleft[M L^{5} T^{1}right] )
C ( cdotleft[M L^{5} T^{-2}right] )
D ( cdotleft[M L^{-1} L^{5} T^{2}right] )
11
29 01.05
10. The length of a cylinder is measured with a meter rod
having least count 0.1 cm. Its diameter is measured with
vernier calipers having least count 0.01 cm. Given that
length is 5.0 cm and radius is 2.0 cm. The percentage error
in the calculated value of the volume will be
(a) 1% (b) 2% (c) 3% (d) 4%
11
30 The dimensional formula of effective
torsional constant of spring is
A ( cdot M^{1} L^{2} T^{-3} )
B. ( M^{1} L^{2} T^{-2} A^{-} )
c. ( M^{1} L^{2} T^{-2} )
D. ( M^{0} L^{0} T^{0} )
11
31 If dimensions of length are expressed
( operatorname{as} G^{x} C^{y} h^{z} ) where ( G, C ) and ( h ) are
universal gravitational constant, speed of light and Planck’s constant respectively. Then This question has multiple correct options
( mathbf{A} cdot x=y )
B. ( x=z )
c. ( y=-3 / 2 )
D. ( z=1 / 2 )
11
32 For the four sets of three measured
physical quantities as given below. Which of the following options is
correct?
( (i) A_{1}=24.36, B_{1}=0.0724, C_{1}= )
( mathbf{2 5 6 . 2} )
( (i i) A_{2}=24.44, B_{2}=16.082, C_{2}= )
( mathbf{2 4 0 . 2} )
( (i i i) A_{3}=25.2, B_{3}=19.2812, C_{3}= )
( mathbf{2 3 6 . 1 8 3} )
( (i v) A_{4}=25, B_{4}=236.191, C_{4}= )
19.5
A. ( A_{1}+B_{1}+C_{1}<A_{3}+B_{3}+C_{3}<A_{4}+B_{4}+C_{4}< )
( A_{2}+B_{2}+C_{2} )
B . ( A_{4}+B_{4}+C_{4}<A_{1}+B_{1}+C_{1}<A_{3}+B_{3}+C_{3}< )
( A_{2}+B_{2}+C_{2} )
c. ( A_{4}+B_{4}+C_{4}<A_{1}+B_{1}+C_{1}=A_{2}+B_{2}+C_{2}= )
( A_{3}+B_{3}+C_{3} )
D. ( A_{1}+B_{1}+C_{1}=A_{2}+B_{2}+C_{2}=A_{3}+B_{3}+C_{3}= )
( A_{4}+B_{4}+C_{4} )
11
33 The Sl unit of form factor is :
A. Ampere
B. volt
c. watt
D. none of the above
11
34 Energy cannot be measured in
A . ( J s )
в. ( W ) s
( c . k W h )
D. erg
11
35 A solution is to be kept between ( 68^{circ} ) F
and ( 77^{circ} ) F. What is the range in temperature in degree Celsius
(C) if the
Celcius / Fahrenheit (F) conversion
formula is given by ( mathbf{F}=frac{9}{5} mathbf{C}+mathbf{3 2} ? )
11
36 Find out the unit and dimentions of the the vander waal’s equation pressure P,V is volume and ( R ) is gas constant: 11
37 The dimension of the universal constant
of gravitation ( G ) is
( mathbf{A} cdotleft[M L^{2} T^{-1}right] )
B. ( left[M^{-1} L^{3} T^{-2}right] )
( mathbf{c} cdotleft[M^{-1} L^{2} T^{-2}right] )
D・ ( left[M L^{3} T^{-2}right] )
11
38 Which row shows a quantity and an
incorrect unit?
( begin{array}{ll}text { quantity } & text { unit } \ text { A. efficiency } & text { no unit } \ text { B. moment of force } & N m^{-1} \ text {C. momentum } & text { Ns } \ text { D. work done } & text { J }end{array} )
11
39 Four students measure a time interval
that is known to be 1.734 s. The measurement recorded by each student is shown. Which measurement is the
most accurate?
A . 1 s
в. 1.7 s
c. 1.83 s
D. 1.604 s
11
40 You measure two quantities as ( A= )
( mathbf{1 . 0 m} pm mathbf{0 . 2 m}, boldsymbol{B}=mathbf{2 . 0 m} pm mathbf{0 . 2 m .} mathrm{We} )
should report correct value for ( sqrt{A B} ) as
A. ( 1.4 m pm 0.4 m )
в. ( 1.41 m pm 0.15 m )
c. ( 1.4 m pm 0.3 m )
D. ( 1.4 m pm 0.2 m )
11
41 14. The dimensional formula for electric potential is
a. [M LT-3A-] b. [MLT-3A-‘]
c. [M LT-3K-] d. none of these
11
42 Which scale is best for measuring the length of a ladybug?
A. Millimeters
B. Centimeters
c. Meters
D. Kilometers
11
43 If a star is ( 5.2 times 10^{16} ) m away. What is
the parallax angle in degrees?
A ( cdot 1.67 times 10^{-4} ) degrees
B . ( 1.67 times 10^{-5} ) degrees
c. ( 0.67 times 10^{-4} ) degrees
D. ( 2.3 times 10^{-4} ) degrees
11
44 15. If the speed v of a particle of mass m as function of time
is given by v = @A sin
where A has dimension
of length.
(a) the argument of trigonometric function must be a
dimensionless quantity
(b) Dimensional formula of wis LT-
(c) Dimensional formula of k is MLT-2
(d) Dimensional formula of is T
m
11
45 The distance between two atoms in a
molecule is measured in order of
Angstrom
A. True
B. False
11
46 Which of the following is the most precise instrument for measuring length?
A. Metre rod of least count ( 0.1 mathrm{cm} )
B. Vernier calipers of least count ( 0.01 mathrm{cm} )
c. Screw gauge of least count ( 0.001 mathrm{cm} )
D. None of these
11
47 Assertion
100 years make 10 decades.
Reason
Every century is divided into 10 decades.
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
48 When a wave traverses a medium the
displacement of a particle located at ( x ) at a time is given by ( y=a sin (b t-c x) ) where a, band are constants of the wave,
which of the following is a quantity with dimensions?
A. ( frac{y}{a} )
в. ( b t )
c. ( c x )
D. ( frac{b}{c} )
11
49 The units of force, velocity and energy are 100 dyne, ( 10 mathrm{cms}^{-1} ) and 500 erg respectively. The units of mass, length and time are:
( A cdot 5 g, 5 mathrm{cm}, 5 mathrm{s} )
B. 5 g, ( 5 mathrm{cm}, 0.5 ) s
c. ( 0.5 mathrm{g}, 5 mathrm{cm}, 5 mathrm{s} )
D. 5 g, ( 0.5 mathrm{cm}, 5 mathrm{s} )
11
50 Which of the following does not have the dimensions of force?
A. Gravitational Potential gradient
B. Energy gradient
c. weight
D. Rate of change of momentummmmmm
11
51 What is the dimensional formula of
universal gravitational’G’? The gravitational force of attraction between two objects of masses
( m_{1} ) and ( m_{2} ) seperated by a distance ( mathrm{d} ) is given by ( boldsymbol{F}=frac{boldsymbol{G} boldsymbol{m}_{1} boldsymbol{m}_{2}}{boldsymbol{d}_{2}} . ) Where ‘G’ is
the universal gravitational constant
B . ( left[M^{-1} L^{2} T^{2}right. )
c. ( left[M^{-1} L^{3} T^{-2}right] )
D. ( left[M^{2} L^{2} T^{-2}right. )
11
52 7. The circular scale of a screw gauge has 50 divisions and pitch
of 0.5 mm. Find the diameter of sphere. Main scale reading
is 2.
A S NA
O ARODB:
5
25
BO8698
M
Fig. 1.9
a. 1.2 mm
c. 2.20 mm
b. 1.25 mm
d. 2.25 mm
(IIT JEE, 2006)
11
53 The dimensions of torque are
( mathbf{A} cdotleft[M L^{3} T^{-3}right] )
В ( cdotleft[M L^{-1} T^{-1}right] )
c. ( left[M L^{2} T^{-2}right] )
D ( cdotleft[M T^{-2}right] )
11
54 The value of ( 500.0 m+600 m m ) with
due regards to significant figures is:
( mathbf{A} .501 m )
в. 500.6 т
c. ( 500.600 m )
D. none of these
11
55 The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate by using the formula ( boldsymbol{P}= )
( boldsymbol{F} / boldsymbol{l}^{2} . ) If the maximum errors in the
measurement of force and length are ( 4 % ) and ( 2 %, ) respectively, then what is the maximum error in the
measurement of pressure?
11
56 A LASER is a source of very intense, monochromatic, and unidirectional
beam oflight. These properties of a laser light can be exploited to measure long distances.The distance of the Moon
from the Earth has been already
determined very preciselyusing a laser as a source of light. A laser light beamed at the Moon takes 2.56 s
to return after reflection at the Moons
surface. How much is the radius of the
lunar orbit around the Earth?
11
57 Fill in the blanks type
Planck’s constant has dimensions
11
58 2. A gas bubble from an explosion under water oscillates
with a period T proportional to pºd’E’, where p is the
static pressure, d is the density of water, and E is the total
energy of the explosion. Find the values of a, b, and c.
(IIT JEE, 1981)
2
.
1
.
1
11
59 The ratio of the weight of a body to its
mass gives the at the given place
A. acceleration due to gravity
B. velocity due to gravity
c. force due to gravity
D. displacement due to gravity
11
60 4. The SI unit of inductance, henry, can be written as
a. Weber/ampere b. Volt-second/ampere
c. Joule/(ampere) d. Ohm-second
11
61 The unit of Planck’s constant is
equivalent to that of :
A. energy
B. angular momentum
c. velocity
D. force
11
62 Dimensional methods provide three major advantages in verification, derivation and changing the system of units. Any empirical formula that is derived based on this method has to be
verified and proportionality constants
found by experimental means. The presence or absence of certain factors –
non dimensional constants or variables
cannot be identified by this method. So every dimensionally correct relation
cannot be taken as perfectly correct. The energy of an SHM is dependent on mass ( m ), frequency ( f ), and amplitude ( A ) of oscillation. The relation is
( mathbf{A} cdot M f / A^{2} )
B. ( M f A^{-2} )
( mathbf{c} cdot M f^{2} A^{-2} )
( mathbf{D} cdot M f^{2} A^{2} )
11
63 If the radius of a sphere is found to be
( 3 c m pm 0.01 c m, ) find the percentage
error in the determination of its volume.
11
64 Match the following two columns.
Column I Column I
11
65 Assertion
Weight of solid in air is ( mathrm{W} ) and in water is ( T=frac{2 W}{3} ) Then relative density of
solid is 3.0
Reason
Relative density of any solid is given by ( R D=frac{text { Weight in air }}{text { Change in weight in water }} )
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
66 The radius of a thin wire is ( 0.16 mathrm{mm} ). The
area of cross-section taking significant figure into consideration in square
millimeters is?
A . 0.0804
B. 0.080
( c cdot 0.08 )
D. 0.080384
11
67 Count total number of S.F. in ( 6.020 times )
( 10^{23} )
A .4
B. 3
( c cdot 6 )
D. 7
11
68 15. A student measures the time period of 100 oscillations of
a simple pendulum four times. The data set is 90 s, 91 s,
95 s and 92 s. If the minimum division in the measuring
clock is 1 s, then the reported mean time should be
(a) 92 +2 s
(b) 92 £ 5.0 s
(c) 92 – 1.8 s (d) 92 + 3 (JEE Main 2016)
11
69 ‘The year 2016 will have February of ( ldots ) days’.
A . 28
B. 29
c. 28.5
D. 30
11
70 State whether true or false.
Equal masses of iron and common salt have different volume.
A. True
B. False
11
71 Write down the number of significant figures in the following value.
( mathbf{0 . 0 6 2 8 c m} )
A . four
B. three
c. ( t w o )
D. one
11
72 Determine the number of significant figure in the following.
( mathbf{0 . 2 3 7 0} mathbf{m} )
11
73 8. A physical quantity x depends on quantities y and z
as follows: x = Ay + B tan (Cz), where A, B, and C are
constants. Which of the followings do not have the same
dimensions?
a. x and B
b. Cand z
c. y and BIA
d. x and A
11
74 23. The value of acceleration due to gravity is 980 cm ,
What will be its value if the unit of length is kilometer
and that of time is minute?
11
75 Which of the following is the parallax angle in the shown diagram?
4
B.
( c )
2
11
76 Boiling point of water on the Celsius scale is
A ( cdot 0^{circ} mathrm{C} )
B. 212^{ } ( mathrm{C} )
c. ( 32^{circ} mathrm{C} )
D. ( 100^{circ} mathrm{C} )
11
77 Brine has a density of ( 1.2 g / c c .40 c c ) of it
are mixed with ( 30 c c ) of water. The
density of solution is
A ( .2 .11 g / c c )
в. ( 1.11 g / c c )
c. ( 12.2 g / c c )
D. ( 20.4 g / c c )
11
78 16. The frequency (n) of vibration of a string is given as
n= 14, where T is tension and I is the length of
n=21m
vibrating string, then the dimensional formula is
a. [MºLT]
b. [M°°T°)
c. [ML-17°
d. [ML°T°
11
79 Match the column
( begin{array}{lll} & text { । } & text { ॥ } \ text { A } & text { Force } & text { erg } \ text { B } & text { Pressure } & text { Kgm } / s^{2} \ text { C } & text { Power } & J s^{-1} \ text {D } & text { Energy } & text { Nm }^{-2}end{array} )
11
80 A unit is so chosen that the numerical
value of a measurement is as small as
possible. True=1; False=0
11
81 The equation of a plane progressive wave is given by ( boldsymbol{y}=boldsymbol{A} sin (boldsymbol{omega} boldsymbol{t}-boldsymbol{k} boldsymbol{x}) )
The dimension of ( (omega / k) ) is that of
A. frequency
B. velocity
c. wavelength
D. inverse of velocity
11
82 State similarities and differences
between the laboratory thermometer
and the clinical thermometer.
11
83 The speed of a car increases uniformly
from zero to ( 10 mathrm{ms}^{-1} ) in ( 2 s ) and then
remain constant.
a. Find the distance travelled by the car
in the first two seconds.
b. Find the distance travelled by the car
in next two seconds.
c. Find the total distance travelled in 4 s.
11
84 Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the
voltage difference are ( 3 % ) each, then
error in the value of resistance of the
wire is
A . ( 6 % )
B. Zero
c. ( 1 % )
D. 3%
11
85 What are the number of signification numbers in ( 0.00034800 ? ) How much is
one astronomical unit in meters?
11
86 A wire has a mass ( 0.3 pm 0.003 g ) and
length ( 6 pm 0.06 ) cm. The maximum
percentage error in the measurements
of its linear mass density is:-
A ( . )
B. 2
( c cdot 3 )
D. 4
11
87 Which of the following numbers has least number of significant figures?
A. 0.80760
00 0066600
B. 0.80200
( c .0 .08076 )
D. 80.267
11
88 The radius of a sphere is ( 1.41 mathrm{cm} ). Its volume to an appropriate number of significant figures is then
( mathbf{A} cdot 11.73 mathrm{cm}^{3} )
B . 11.736 ( c m^{3} )
( mathrm{c} cdot 11.7 mathrm{cm}^{3} )
D. ( 117 mathrm{cm}^{3} )
11
89 The mass of a box measured by a
grocer’s balance is 2.3 kg.two gold pieces of masses ( 20.15 g ) and ( 20.17 g )
are added to the box. The total mass of
the box is:
A . ( 2.30 mathrm{kg} )
в. ( 2.340 mathrm{kg} )
c. ( 2.34 mathrm{kg} )
D. ( 2.3 mathrm{kg} )
11
90 e following quantities has its unit as newton-
19. Which of the following quantiti
second?
a. Energy
b. Torque
c. Momentum
d. Angular momentum
11
91 decimeter is ( _{–} ) megameter.
A ( cdot 10^{-7} )
B. ( 10^{-6} )
( mathrm{c} cdot 10^{-5} )
D. ( 10^{-8} )
11
92 When two liquid of same volume but
different densities ( rho_{1} ) and ( rho_{2} ) are mixed
together, then the density of the mixture is
A ( cdot frac{p_{1}+p_{2}}{2} )
B . ( p_{1}+p_{2} )
c. ( frac{2 p_{1} p_{2}}{p_{1}+p_{2}} )
D. ( 2 p_{1}+2 p_{2} )
11
93 The accuracy in the measurement of the diameter of hydrogen atom measured as ( 1.06 times 10^{-10} mathrm{m} ) is :
A .0 .01
В. ( 106 times 10^{-10} )
c. ( frac{1}{106} )
D. ( 0.01 times 10^{-10} )
11
94 The dimensional formula for Young’s
modulus is :
( mathbf{A} cdotleft[M L^{-1} T^{-2}right] )
B ( cdotleft[M^{0} L T^{-2}right] )
( mathbf{c} cdotleft[M L T^{-2}right] )
D. ( left[M L^{2} T^{-2}right] )
11
95 Choose the correct answer from the
following
This question has multiple correct options
A. An area of one square centimetre is ( 10^{4} ) times greater
than one square metre.
B. 1 hour 18 min is equal to 3618 seconds
C. Sl unit of volume is cubic metres.
D. Metre is the standard unit to measure length.
11
96 The side of a cube is 2.5 metre, the volume of the cube to the correct
significant figures is :
A . 15
B. 16
( c cdot 1.5 )
D. 1.6
11
97 The force of interaction between two
atoms is given by ( boldsymbol{F}=boldsymbol{alpha} boldsymbol{beta} exp left(-frac{boldsymbol{x}^{2}}{boldsymbol{alpha k t}}right) )
where ( x ) is the distance, ( k ) is the
Boltzman constant and ( boldsymbol{T} ) is
temperature and ( alpha ) and ( beta ) are two
constants. The dimension of ( beta ) is
A ( cdot M^{2} L^{2} T^{-2} )
B. ( M^{2} L T^{-4} )
c. ( M^{0} L^{2} T^{-4} )
D. ( M L T^{-2} )
11
98 1 nano metre ( (1 mathrm{nm}) ) is equal to
( mathbf{A} cdot 10^{-7} mathrm{m} )
В. ( 10^{-9} mathrm{m} )
( mathbf{c} cdot 10^{9} mathrm{m} )
D. None of these
11
99 Select correct definition of light year:
A. The distance travelled by the light in a year
B. The distance travelled by the atoms in a year
C. The distance travelled by the earth in a year
D. The distance travelled by the sound in a year
11
100 The order of magnitude of 0.00701 is:
A . –
B. – –
( c cdot 2 )
D.
11
101 A calorimeter has mass 100 g and
specific heat ( 0.1 mathrm{kcal} / mathrm{kg}^{circ} mathrm{C} ). It contains
250 gm of liquid at ( 30^{circ} C ) having
specific heat of ( 0.4 mathrm{kcal} / mathrm{kg}^{circ} mathrm{C} ). If we
drop a piece of ice of mass ( 10 mathrm{g} ) at ( 0^{circ} mathrm{C} )
What will be the temperature of the mixture?
11
102 Show that the frictional error in the ( n^{t h} )
power of a quantity is equal to n times the fractional error in the quantity itself
State the general rule for evaluating the error in a combined calculation.
11
103 5. A body travels uniformly a distance of (13.8 +0.2) m in
a time (4.0 +0.3) s. The velocity of the body within error
limits is
(a) (3.45 + 0.2) ms- (b) (3.45 + 0.3) ms-1
(c) (3.45 + 0.4) ms-1 (d) (3.45 +0.5) ms-
11
104 The dimensional formula of ( frac{1}{2} mu_{0} H^{2}left(mu_{0}right. ) Permeability of free space and ( mathrm{H} ) magnetic field intensity) is:
A ( cdot M L T^{-1} )
B. ( M L^{2} T^{-2} )
c. ( M L^{-1} T^{-2} )
D. ( M L^{2} T^{-1} )
11
105 If ( y=sin theta, ) then for what value of ( theta, ) the
relative error in y is minimum?
A ( cdot 90^{circ} )
в. ( 30^{circ} )
( c cdot 0^{0} )
D. ( 45^{circ} )
11
106 Á is equal to:
( mathbf{A} cdot 0.1 mathrm{nm} )
B . ( 10^{-10} mathrm{cm} )
( mathbf{C} cdot 10^{-8} m )
( mathbf{D} cdot 10^{-4} mu )
11
107 Show dimensionally that the expression, ( boldsymbol{Y}=frac{boldsymbol{M} boldsymbol{g} boldsymbol{L}}{boldsymbol{pi} boldsymbol{r}^{2} boldsymbol{l}} ) is
dimensionally correct, where Y is Young’s modulus of the material of wire,
Lis length of wire, Mg is the weight applied on the wire and I is the increase in the length of the wire.
11
108 11. Which of the following represents a volt?
(a) Joule/second (b) Watt/Ampere
(c) Watt/Coulomb (d) Coulomb/Joule
11
1
11
109 A calorie is a unit of heat energy and its
value is ( 4.18 mathrm{J} ) where ( 1 J=1 k g m^{2} s^{-2} )
Suppose we use a new system of units in which unit of mass equals ( boldsymbol{alpha} ) kg, the
unit of length equals ( beta mathrm{m} ) and the unit
of the time is ( gamma ) sec. Then the value of a
calorie in the new system of units is
then
A ( cdot ) 4.18 ( frac{gamma^{2}}{alpha beta^{2}} )
B. ( 4.18 frac{alpha beta^{2}}{gamma^{2}} )
c. ( 4.18 frac{gamma^{2}}{alpha} )
D. ( 4.18 frac{beta^{2}}{alpha gamma^{2}} )
11
110 If ( mathrm{E}, mathrm{m}, mathrm{I} ) and ( mathrm{G} ) denote energy, mass,
angular momentum and gravitational constant respectively, then the quantity ( left(frac{E l^{2}}{m^{5} G^{2}}right) ) has the dimensions of then
A. mass
B. length
( c . ) time
D. angle.
11
111 3. What is the number of significant figures in 0.310×10°?
(2) 2 (b) 3 (c) 4 (d) 6
11
112 Match the physical quantities given in
Column I with suitable dimensions
expressed in Column II.
Column Column I II
a) Angular momentum
g) ( M L^{2} T^{-2} )
Latent heat
h) ( M L^{2} Q^{-2} )
b)
Torque ( M L^{2} T^{-1} )
c)
i)
d) Capacitane
j) ( M L^{3} T^{-1} Q^{-2} )
Inductance
k)
e) ( M^{-1} L^{-2} T^{2} Q^{2} ) ( L^{-2} T^{2} Q^{2} )
( f) )
Resistivity ।) ( L^{2} T^{-2} ) ( T )
A. a-i, b-l, c-g, d-k, e-h, f-j
B. a-l, b-i, c-k, d-g, e-j, f-h
c. a-i, b-l, c-h, d-j, e-g, f-k
D. a-h, b-j, c-g, d-k, e-i ( f- )
11
113 A star’s distance ( (d) ) and its parallax angle ( (p) ) are related to each other as:
A ( cdot d=frac{1}{p} )
в. ( d=frac{1}{p^{2}} )
c. ( _{p}=frac{1}{d^{2}} )
D. none of these
11
114 A physical quantity ( times ) is calculated from the relation ( boldsymbol{x}=frac{boldsymbol{a}^{2} boldsymbol{b}^{3}}{boldsymbol{c} sqrt{boldsymbol{d}}} )
percentage error in ( a, b, c ) and ( d ) are ( 2 %, 1 %, 3 % ) and ( 4 % ) respectively. What
is the percentage error in ( x ? )
11
115 The decrease in percentage error:
A. increases the accuracy
B. does not effect the accuracy
C. decreases the accuracy
D. both ( A ) and ( C )
11
116 If the magnitude of mass is 1 kg that of time is 1 minute and that of
acceleration due to gravity is ( 10 mathrm{ms}^{-2} ) the magnitude of energy injoule
A ( .3 .6 times 10^{5} )
В. ( 3.6 times 10^{-5} )
c. ( 3.6 times 10^{2} )
D. 10
11
117 toppr
Q Type your question
current which is then converted into a
digital readout on the display. The electric circuit gives a current of
2.0 mA when a weight of 30N is applied,
and a current of ( 0.5 mathrm{mA} ) when a weight of ( 5 mathrm{N} ) is applied

Which calibration curve could represent
this circuit?
( A )
B.
( c )
( D )

11
118 Assertion
A light-year is a distance that light
travels with velocity of ( 3 times 10^{8} m s^{-1} ) in
one year.
Reason
Light year is the unit for measuring time.
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
119 In particular system of unit, if the unit of mass becomes twice and that of time
becomes half, then 8 Joules will be
written as
A . 16
B.
( c cdot 4 )
D. 64
11
120 Dimensions of impulse are:
A ( . M L T^{-2} )
В. ( M^{2} L T^{-1} )
( mathrm{c} cdot M L T^{-1} )
D. ( M L^{2} T^{-1} )
11
121 6. a. Calculate the area enclosed by a circle of radius 0.56 m
to the correct number of significant figures.
b. Calculate the area enclosed by a circle of diameter
1.12 m to the correct number of significant figures.
A1 2010-
6A10-5.1
11
122 The density of a body is represented by the expression:
Where ( V ) is the volume and ( M ) is the
mass of a body
A ( cdot D=frac{V}{M} )
B. D=M X V
c. ( _{D}=frac{1}{M times V} )
D. ( D=frac{M}{V} )
11
123 Are senses reliable for accurate
measurement?
A . True
B. False
11
124 The percentage errors in the measurement of the length (L) and breadth (B) of a rectangle are ( ell ) and ( b % ) respectively. Then the percentage error in the calculation of the area will be
( A cdot(mid b) % )
B. (1+b)%
( c cdot(L+1)(B+b) )
D. Lb+BL
11
125 3. Dimensional formula ML-T2 does not represent the
physical quantity
(a) Young’s modulus of elasticity
(b) Stress
(c) Strain
(d) Pressure
11
126 10. If the velocity of light (c), gravitational constant (G) and
Planck’s constant (h) are chosen as fundamental units, then
the dimensions of mass in new system is
(a) (1/2G1/21/2
(b) c1/2G1/2h-1/2
(c) 01/2G-1/2h1/2
(d) c-1/2G1/2h1/2
11
127 The relation between force ‘ ( F ) ‘ and
density ‘ ( d ) ‘ is ( F=frac{x}{sqrt{d}} . ) The dimensions
of ( x ) are:
( mathbf{A} cdotleft[L^{-1 / 2} M^{3 / 2} T^{-2}right] )
B ( cdotleft[L^{-1 / 2} M^{1 / 2} T^{-2}right] )
( mathbf{C} cdotleft[L^{-1} M^{3 / 2} T^{-2}right] )
D・ ( left[L^{-1} M^{1 / 2} T^{-2}right] )
11
128 State the S.I. units of mass and weight.
A. gand kg
B. kg and g
c. ( mathrm{kg} ) and ( mathrm{N} )
D. ( mathrm{N} ) and ( mathrm{kg} )
11
129 The nearest star to our solar system is
4.29 light years away. How much is this distance in terms of parsecs? How
much parallax would this star (named Alpha Centauri) show when viewed from
two locations of the Earth six months
a part in its orbit around the Sun?
11
130 The period of oscillation of a simple pendulum is ( T=2 pi sqrt{L / g} . ) Measured
value of ( L ) is ( 20.0 mathrm{cm} ) known to ( 1 mathrm{mm} )
accuracy and time for 100 oscillations of
the pendulum is found to be 90 s using a wrist watch of 1 sec resolution. What is
the accuracy in the determination of
11
131 If ( L ) and ( R ) denote inductance and
resistance then dimension of ( L / R ) is
( mathbf{A} cdotleft[M^{0} L^{0} T^{0}right] )
в. ( left[M^{0} L^{0} Tright] )
( mathbf{c} cdotleft[M^{2} L^{0} T^{2}right] )
D cdot ( left[M L T^{2}right]^{2} )
11
132 7. Suppose refractive index u is given as
B
u= A+
22
where A and B are constants and 2 is wavelength, then
dimensions of B are same as that of
a. Wavelength
b. Volume
c. Pressure
d. Area
11
133 If the dimension of a physical quantity is given by ( left[M^{a} L^{b} T^{c}right] ) then the physical
quantity will be
A. acceleration, if ( a=1, b=-1, c=-2 )
B. velocity, if ( a=1, b=0, c=-1 )
c. pressure, if ( a=1, b=-1, c=-2 )
D. force, if ( a=0, b=-1, c=-2 )
11
134 The radius of a sphere is measured to be ( 5.3 pm 0.1 mathrm{cm} . ) Calculate the
percentage error in the measurement of
its volume.
A . ( 3.45 % )
B . ( 5.66 % ) %
c. ( 2.4 % )
D. 1.05%%%%
11
135 If ( I ) is regarded as the fourth dimension, then the dimensional formula of charge
in terms of current ( boldsymbol{I} ) is
( mathbf{A} cdotleft[I T^{2}right] )
B . ( left[I^{0} T^{0}right] )
c. ( left[I^{-1} T^{0}right] )
D. [IT]
11
136 What is the minimum and maximum
unit of measurement of mass?
11
137 Count total number of significant figures in 3500
( mathbf{A} cdot mathbf{1} )
B. 2
( c cdot 3 )
( D )
11
138 The radius of a sphere is measured to be ( (2.1 pm 0.5) c m . ) Calculate its surface
area with error limits.
11
139 Which of the statements are false?
A. The units of physical quantity represented by volume is ( c m^{3} )
B. The unit of physical quantity represented by mass is ( operatorname{ton} )
C the work done is represented by ( frac{k g}{m} )
D. The unit of physical quantity represented by weight is Newton
11
140 Illustration 1.22 The period of oscillation of a simple
pendulum in the experiment is recorded as 2.63
2.56 4,242 s, 2.71 s, and 2.80 s. Find the average absolute
error,
11
141 If ( P ) represents radiation pressure,
represents speed of light and ( mathrm{Q} ) represents radiation energy striking a
unit area per second, then non-zero
integers ( x, y ) and ( z, ) such that ( P^{x} Q^{y} c^{z} ) is dimensionless, may be
A. ( x=1, y=1, z=1 )
B. ( x=1, y=-1, z=1 )
c. ( x=-1, y=1, z=1 )
D. ( x=0, y=0, z=0 )
11
142 Illustration 1.8 Let us check the dimensional correctness of
the relation v = u + at.
11
143 A thin bar magnet of length ( 2 L ) is bent at the mid-point so that the angle
between them is ( 60^{circ} . ) The new length of
the magnet is
A ( cdot sqrt{2} L )
B. ( sqrt{3} L )
( c cdot 2 L )
D. ( L )
11
144 Which of the following is not a vector quantity?
A. Distance
B. Displacement
c. Acceleration
D. Velocity
11
145 A SONAR (sound navigation and ranging) uses ultrasonic waves to
detect and locate objects under water In a submarine equipped with a SONAR the time delay between generation of a probe wave and the reception of its echo after reflection from an enemy
submarine is found to be 77.0 s. What is
the distance of the enemy submarine?
(Speed of sound in water ( =1450 m s^{-1} ) ).
11
146 A body of weight ( W_{1} ) is suspended from
the celling of a room through a chain of
weight ( W_{2} ) The earth pulls the chain by a force equal to:
( A cdot W_{2} )
B. ( left(W_{1}+W_{2}right) / 2 )
( mathbf{c} cdotleft(W_{1}+W_{2}right) )
D. ( W_{1} times W_{2} )
11
147 The dimensions of Planck’s constant
are
( mathbf{A} cdotleft[M L^{-3} T^{-1}right] )
в. ( left[M L^{-2} T^{-1}right] )
( mathbf{c} cdotleft[M^{0} L^{-1} T^{-3}right. )
D・ ( left[M L^{2} T^{-1}right] )
11
148 The wavelength of light of a particular colour is 5800 A. What is its order of
magnitude in meter?
11
149 1 fermi is equal to
( mathbf{A} cdot 10^{-15} mathrm{m} )
B. ( 10^{15} mathrm{m} )
( mathbf{C} cdot 10^{-12} mathrm{m} )
( D cdot 10^{12} m )
11
150 The best method to reduce random error
is
A. To change the instrument used for the measurement
B. To take help of experienced observer
C. To repeat the experiment many times and to take the average results
D. None of the above
11
151 If weight of an object in air ( W_{a} ) is
( (10.0 pm 0.1) g ) and its weight in water
( W_{L} ) is ( (5.00 pm 0.2) g, ) then percentage
error in its relative density is? ( left(text { Relativedensity }=frac{W_{a}}{W_{a}-W_{L}}right) )
A . ( 2 % )
B. ( 5 % )
c. ( 7 % )
D. ( 1.5 % )
11
152 1 x and a stand for distance, then for what value of n is
the given equation dimensionally correct? The equation
dx
sin-1
a. O
c. -2
b. 2
d. 1
11
153 If surface tension (S), Moment of inertia
(I) and Planck’s constant (h), were to be taken as the fundamental units, the
dimensional formula for linear
momentum would be :-
A ( cdot S^{3 / 2} I^{1 / 2} h^{0} )
B. ( S^{1 / 2} I^{1 / 2} h^{0} )
c. ( S^{1 / 2} I^{1 / 2} h^{-1} )
( mathbf{D} cdot S^{1 / 2} I^{3 / 2} h^{-1} )
11
154 If the force is given by ( boldsymbol{F}=boldsymbol{a} boldsymbol{t}+boldsymbol{b} boldsymbol{t}^{2} ) with ( boldsymbol{t} )
as time. The dimensions of a and b are:
( mathbf{A} cdotleft[M L T^{-4}right],left[M L T^{-2}right. )
B . ( left[M L T^{-3}right],left[M L T^{-4}right] )
C ( cdotleft[M L^{2} T^{-3}right],left[M L^{2} T^{-2}right] )
D cdot ( left[M L^{2} T^{-3}right],left[M L^{3} T^{-4}right] )
11
155 If velocity ‘ ( V ) ‘, kinetic energy ‘ ( k ) ‘ and
time ‘T” are taken as fundamental
quantities, then the dimensional
formula of surface tension is:
A ( cdot K V^{2} T^{2} )
B. ( K V^{-2} T^{-2} )
c. ( K^{2} V^{2} T^{-2} )
D. ( K^{2} V^{-2} T^{-2} )
11
156 Write the number of significant digits in ( 6.032 ? )
A . 4
B. 3
( c cdot 2 )
D. none of the above
11
157 What is the order of magnitude of one
light year?
( mathbf{A} cdot 10^{15} m )
B . ( 10^{10} m )
c. ( 9.2 times 10^{15} mathrm{m} )
D. ( 10^{16} m )
11
158 By rounding off,
(a) 20.96 and ( (b) )
0.0003125 to three significant figures, we get
A ( cdot 21.0 ; 312 times 10^{-4} )
B . ( 21.0 ; 3.125 times 10^{-4} )
c. ( 2.10 ; 3.12 times 10^{-4} )
D. ( 210 ; 3.12 times 10^{-4} )
11
159 Parallax method is based on which of
the following principle?
A. Disparity
B. Lutz Kelker bias
c. Trilateration
D. Triangulation
11
160 Which of the following relations for the displacement of a partide undergoing simple harmonic motion is not correct
dimensionally?
A ( cdot Y=a sin frac{2 pi t}{T} )
B. ( Y=a cos omega t )
c. ( Y=frac{a}{T} sin left(frac{t}{a}right. )
( V=a sqrt{2}left(sin frac{2 pi t}{T}+cos frac{2 pi t}{T}right) )
11
161 State the uses of dimensional analysis
using dimensions, show that 1 joule ( = ) ( mathbf{1 0}^{mathbf{7}} ) erg
OR
Explain different types of errors in
measurement.

An object was weighed by a physical balance and following readings were obtained
( 5.04 g, 5.06 g, 4.17 g, 5 g m, 4.93 g m )
Find
1.) Mean absolute error
2.) percentage error

11
162 INICIIUDICIUL
18. The dimensions of power are
f
lere
11
163 Work done is a ( _{–}- ) – quantity
A. vector
B. scaler
c. constant
D. fundamental
11
164 Anushka noted down the following observations in her practical book.
i. Weight of the metal block in air ( =260 )
( boldsymbol{g}-boldsymbol{w} boldsymbol{t} )
i ( i . ) Weight of the metal block in water ( = ) ( 220 g-w t )
iii. Weight of the metal block in salt
water ( =180 g-w t )
Find the relative density of the salty
water
11
165 1 ULUU
35. The time dependence of a physical quantity P is given by
P= Pre-or’, where a is a constant and t is time. Then
constant a is/has
a. Dimensionless b. Dimensions of T-4
c. Dimensions of
P d . Dimensions of T
11
166 The Sl unit of atmospheric pressure is
A. Barye
B. Pascal
c. Dyne
D. None of the above
11
167 1. To find the distance d over which a signal can be seen
clearly in foggy conditions, a railways engineer uses
dimensional analysis and assumes that the distance
depends on the mass density pof the fog, intensity (power/
area) S of the light from the signal and its frequency f. The
engineer finds that d is proportional to Sh. The values of
nis
(JEE Advanced, 2014)
11
168 If ( L ) has the dimensions of length, ( V )
that of potential and ( epsilon_{0} ) is the permittivity of free space then quantity
( L V epsilon_{0} ) has the dimensions of:
A . current
B. charge
c. resistance
D. voltage
11
169 Accuracy defines nearness of a measured value to the standard or true
value. If true enter 1 else enter 0
11
170 Which of the following is not the name of a physical quantity?
A. Displacement
B. Momentum
c. Meter
D. Torque
11
171 State whether given statement is True or False.
The standard quantity used for comparison is called fundamental quantity.
A. True
B. False
11
172 The standard quantity used for comparison is called
A. Scale
B. Unit
c. Magnitude
D. All
11
173 Convert the given measurement into the bigger unit. Then, multiply by the second number and find the products.
( 43 g 732 m g ) and 18
11
174 Which of the following is not a characteristic of the standard unit?
A. It should be of convenient size
B. It should change with respect to space and time
c. It should not be perishable
D. It should be eerily reproducible
11
175 The S.I. unit of pressure is pascal
A. True
B. False
11
176 1 Newton ( =K ) dyne, then what is the
value of ( boldsymbol{K} ) ?
A . 1
B. ( 10^{2} )
( c cdot 10^{5} )
D. 10
11
177 The diameter of a sphere is measured with an instrument having least count ( 0.001 mathrm{cm} . ) The diameter is ( 1.933 mathrm{cm} . ) The
radius to correct significant figures will
be:
A . ( 0.9665 mathrm{cm} )
B. ( 0.966 mathrm{cm} )
c. ( 0.967 mathrm{cm} )
D. none of these
11
178 8. If energy (E), velocity (v) and force (F) be taken as
fundamental quantity, then what are the dimensions of
mass
(a) Ev2 (b) Ev-2 (c) Fv-1 (d) Fv-2
11
179 A cube has a side of length ( 1.2 times 10^{-2} . ) Its volume upto correct significant figures is
A . ( 1.7 times 10^{-6} m^{3} )
В . ( 1.73 times 10^{-6} m^{3} )
( mathbf{c} cdot 1.78 times 10^{-6} m^{3} )
D. ( 1.732 times 10^{-6} mathrm{m}^{3} )
11
180 ILLUSTRATION 33.3
Read the screwgauge shown below:
20
E
40
TITIE
mm
Object thickness (1/2 mm
= 6.5 mm + 14
Object thickness = 4.5 mm +39
om 20/1/2 mm
50
= 4.89 mm
(50
11
181 ( mathbf{1} N=Z k g f ) (approx.), then what is the
value of ( Z ) ?
A . ( 0 . )
B.
( c cdot 10 )
D.
11
182 Illustration 1.2 Convert 1 joule to ergs. 11
183 6. The mass and volume of a body are 4.237 g and 2.5 cm,
respectively. The density of the material of the body in
correct significant figures is
(a) 1.6048 g cm. (b) 1.69 g cm
(c) 1.7 g cm
(d) 1.695 g cm
1:
11
184 A thermometer placed under the armpit always shows a lower value than the actual body temperature. Which type of error is demonstrated in its
measurement.
11
185 The length and breadth of a metal sheet are ( 3.124 m ) and ( 3.002 m ) respectively.
The area of this sheet upto four correct
significant figure is :
A ( .9 .378 mathrm{m}^{2} )
В. ( 9.37 m^{2} )
c. ( 9.378248 mathrm{m}^{2} )
D. ( 9.3782 mathrm{m}^{2} )
11
186 11. A Vernier callipers has 1 mm marks on the main scale. It
has 20 equal divisions on the vernier scale, which match
with 16 main scale divisions. For this Vernier callipers,
the least count is
a. 0.02 mm b. 0.05 mm c. 0.1 mm d. 0.2 mm
(IIT JEE, 2010)
11
187 A solid cube has volume ( (1000 pm 0.3) )
( c m^{3} . ) The side of the cube is
A ( cdot(10 pm 0.1) ) ст
в. ( (10 pm 0.01) ) ст
c. ( (10 pm 0.001) mathrm{cm} )
D. ( (10 pm 0.003) ) с ( m )
11
188 State whether True or False:
Vector Quantities obey law of ordinary algebra.
A. True
B. False
11
189 The radius of a hydrogen atom is ( 0.5 dot{A} ). Find the order of magnitude of volume
of one hydrogen atom is ( 10^{-10 x} ). The
value of ( x ) is:
11
190 The dimension of the ratio of angular
momentum to linear momentum is
( mathbf{A} cdot L^{0} )
B . ( L^{1} )
c. ( L^{2} )
D. ( M L T )
11
191 DUw all CUITUL
11. If L = 2.331 cm, B = 2.1 cm, then L + B =
(a) 4.431 cm
(b) 4.43 cm
(c) 4.4 cm
(d) 4 cm
TJI
ion
11
192 Which of the following pairs has not the same dimension?
A. Stress; pressure
B. Force; surface tension
c. Impulse; linear momentum
D. Frequency; angular velocity
11
193 3. Some physical quantities are given in Column 1 and
some possible SI units in which these quantities may be
expressed are given in Column II. Match the physical
quantities in Column I with the units in Column II.
i.
a.
(volt) (co
ii.
Column I
GMM,
3RTIM
Flq?B?
GMJR,
Column II
(volt) (coulomb) (metre)
b. (kilogram) (metre) (second) ?
c. (meter)? (second) 2
d. (farad) (volt)?(kg)-!
iv.
where G is universal gravitational constant; M, mass of the
earth; M, mass of sun; Re, radius of the earth; R, universal
gas constant; T, absolute temperature; M, molar mass; F,
force; 9, charge; B, magnetic field. (IIT JEE, 2007)
11
194 2. The dimensions of constant b are
a. MLT-2
b. ML-T-2
c. L.
d. Lý
11
195 5. A wire of length/=6+0.06 cm and radius r=0.5 +0.005 cm
has mass m=0.3 + 0.003 g. Maximum percentage error
in density is
b. 2
c. 1
d. 6.8
(UIT JEE, 2004)
domingos
ho
2000)
11
196 Hertz is the unit of
A. wavelength
B. amplitude
c. frequency
D. None of these
11
197 Turpentine oil is flowing through a tube of length I and radius r. The pressure difference between the two ends of the
tube is p. The viscosity of oil is given ( boldsymbol{eta}=frac{boldsymbol{p}left(boldsymbol{r}^{2}-boldsymbol{x}^{2}right)}{boldsymbol{4} boldsymbol{v} boldsymbol{l}}, ) where ( mathbf{v} ) is velocity of oil
at a distance ( x ) from the axis of the tube.
The dimensional formula of viscosity is
( mathbf{A} cdotleft[M^{0} L^{0} T^{0}right] )
B . ( left[M^{1} L^{-1} T^{-1}right] )
( mathbf{c} cdotleft[M L^{2} T^{-1}right] )
D cdot ( left[M^{-1} L^{-1} T^{1}right] )
11
198 Let ( left[epsilon_{0}right] ) denote the dimensional formula
of the permittivity of vacuum. If ( boldsymbol{M}= ) mass, ( boldsymbol{L}= ) length ( , boldsymbol{T}=boldsymbol{t} ) ime and ( boldsymbol{A}= )
electric current, then
( mathbf{A} cdot epsilon_{0}=left[M^{-1} L^{-3} T^{2} Aright] )
B . ( epsilon_{0}=left[M^{-2} L^{-3} T^{4} A^{2}right. )
C ( . epsilon_{0}=left[M^{1} L^{2} T^{1} A^{2}right] )
D. ( epsilon_{0}=left[M^{1} L^{2} T^{1} Aright] )
11
199 C. 4%
d. 5%
75. The relative density of a material is found by weighing the
body first in air and then in water. If the weight in air is
(10.0 + 0.1) gf and the weight in water is (5.0+ 0.1) gf,
then the maximum permissible percentage error in relative
density is
a. I
b . 2
c. 3
d. 5
10_
1.foberianlantiri
11
200 UN)
a. )
potential energy of a particle varies with distance
Ax1/2
x as U=
=, where A and B are constants. The
, where A and
x² + Blo
dimensional formula for A x B is
a. M’/7/27-2
b. ML11/21-2
c. M'[5127-2
d. M 19/2T-2
11
201 A student performs an experiment for determination of ( gleft(=frac{4 pi^{2} l}{T^{2}}right), l approx 1 m )
and he commits an error of ( Delta l ). For T he
takes the time of n oscillations with the
stop watch of least count ( Delta T ) and the
commits a human error of 0.1 sec. For
which of the following data, the measurement of ( g ) will be most
accurate?
A. ( Delta l-5 m m, Delta T-0.2 sec , n-10 ), Amplitude of oscillation ( 5 mathrm{mm} )
B. ( Delta l=5 m m, Delta T-0.2 ) sec ( , n-20, ) Amplitude of oscillation-
( 5 mathrm{mm} )
c. ( Delta l-5 m m, Delta T-0.1 sec , n- )
( 20, ) Amplitude of oscillation ( 1 mathrm{mm} )
D. ( Delta l ) -1mm, ( Delta T ) -0.1sec, ( n-50 ), Amplitude of oscillation-
( mathrm{mm} )
11
202 Count total number of S.F. in ( 1.60 times )
( mathbf{1 0}^{-19} )
( A cdot 3 )
B. 5
( c cdot 2^{-} )
D. 22
11
203 2. Select the pair whose dimensions are same
(a) Pressure and stress (6) Stress and strain
(c) Pressure and force (d) Power and force
11
204 29. It has been observed that velocity of ripple waves produced
in water depends upon their wavelength (a), density of
water (P), and surface tension (T). Prove that ve o Tlap.
11
205 The number of significant figures in ( mathbf{5 . 6 9} times mathbf{1 0}^{mathbf{1 5}} mathbf{k g} ) is
( mathbf{A} cdot mathbf{1} )
B . 2
( c .3 )
D. 18
11
206 The farthest objects in our universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in ( k m ) of a quasar from which light takes 3.0
billion years to reach us?
11
207 27. The period of oscillation of a simple pendulum is
T = 21
. L is about 10 cm and is known to 1 mm
accuracy. The period of oscillation is about 0.5 s. The time
of 100 oscillations is measured with a wrist watch of 1 s
resolution. What is the accuracy in the determination of
??
11
208 Calculate area enclosed by a circle of
diameter ( 1.06 ~ m ) to correct number of
significant figures.
A. ( 0.883 m^{2} )
В. ( 0.0883 m^{2} )
с. ( 0.88333 m^{2} )
D. ( 0.8830 m^{2} )
11
209 ‘POISE’ is the:
A. C.G.S. unit of surface tension
B. C.G.S. unit of viscosity
C. M.K.S. unit of viscosity
D. M.K.S. unit of surface energy
11
210 A substance of mass ( 49.53 g ) occupies
( 1.5 mathrm{cm}^{3} ) of volume. The density of the
substance (in ( g c m^{-3} ) ) with correct number of significant figures is :
A. 3.3
B. 3.302
c. 3.30
D. 3.300
11
211 The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure
difference across the ends) ( ^{n} ) and
(average velocity of the liquid ) ( ^{m} ). Which
of the following relations between ( boldsymbol{m} )
and ( n ) is correct?
A ( . m=n )
B. ( m=-n )
c. ( m^{2}=n )
D. ( m=-n^{2} )
11
212 со портоосоо
6. If a kilogram, ß meter, and y second are the fundamental
units, 1 cal can be expressed in new units as [1 cal = 4.2 J]
a. a’ By b. alß?y c. 4.2a-‘ß d. 4.20 ß?y
face
11
213 The energy ( E ) of an oscillating body in simple harmonic motion depends on its
mass ( m ), frequency ( n ) and amplitude ( a )
Using the method of dimensional analysis find the relation between
( boldsymbol{E}, boldsymbol{m}, boldsymbol{n} ) and ( boldsymbol{a} )
A ( cdot E=k m n^{2} a^{2}(k=a text { dimensionless constant }) )
B . ( E=k m^{2} n^{2} a^{3}(k=a text { dimensionless constant }) )
C . ( E=k m^{1} n^{1} a^{2}(k=a text { dimensionless constant }) )
D. ( E=k m^{2} n^{1} a^{2}(k=a text { dimensionless constant }) )
11
214 What is meant by Precision? 11
215 Write the number of significant digits
in 100.10
11
216 Which of the following is used as ( mathrm{S} ) I prefixes:
A. Femto
B. Atto
c. zepto
D. All of the above
11
217 Which of the following quantities has a unit but dimensionless?
A. Strain
B. Reynolds number
c. Angular displacement
D. Poisson’s ratio
11
218 Angular diameter of the Jupiter is ( 36 ” . )
the distance of the Jupiter form the
Earth is 825 million kilometer, find the diameter of Jupiter.
11
219 A student measure the thickness of an
object by three different instruments and gets the result as ( 0.5 mathrm{cm}, 0.50 mathrm{cm} ) ( 0.500 mathrm{cm} . ) State the one which is more
accurate.
A . ( 0.5 mathrm{cm} )
B. ( 0.50 mathrm{cm} )
c. ( 0.500 mathrm{cm} )
D. All the measurements are equally accurate.
11
220 Force ( boldsymbol{F} ) is given in terms of time ( t ) and
distance ( boldsymbol{x} ) by ( boldsymbol{F}=boldsymbol{A} boldsymbol{operatorname { s i n }} boldsymbol{C t}+boldsymbol{B} cos boldsymbol{D} boldsymbol{x} )
Then the dimensions of ( frac{A}{B} ) and ( frac{C}{D} ) are given by :
A ( cdot M L T^{-2}, M^{circ} L^{circ} T^{-} )
B. ( M L T^{-2}, M^{circ} L^{-1} T^{c} )
c. ( M^{circ} L^{circ} T^{circ}, M^{circ} L^{1} T^{-1} )
D. ( M^{circ} L^{1} T^{-1}, M^{circ} L^{circ} T^{circ} )
11
221 If the absolute errors in two physical
quantities ( A ) and ( B ) are ( a ) and ( b ) respectively, then the absolute error in
the value of ( A B ) is:
[Disclaimer: The options in the original question have been changed to match with the actual solution / answer.
( mathbf{A} cdot b B-a A )
B. ( a A+b B )
( mathbf{c} cdot a B+b A )
( mathbf{D} cdot a B-b A )
11
222 The three physical quantities ( x, y ) and ( z )
have units ( g quad c m^{2} s^{-5}, g s^{-1} ) and ( c m s^{-2} ) respectively.
The relation between ( x, y ) and ( z ) is
A ( cdot x=y z^{2} )
B . ( x=y^{2} x )
c. ( y^{2}=x z )
D. ( z=x^{2} y )
11
223 Fill in the blank:
When the measured quantity is not dimensionless, is a
dimensionless error.
A. gross error
B. absolute error
c. instrumental error
D. relative error
11
224 11. The dimensions of magnetic field in M, L, T and C
(Coulomb) is giving as
(a) [MT-c-‘i (b) [MT-2 0-1
(c) [MLT-C- (d) [MT2 C-21 (AIEEE 2008)
11
225 In order to find the density of a solid we have to first know its :
( A . ) mass and area
B. weight and area
c. shape and volume
D. mass and volume
11
226 17. The dimensional formula of angular velocity is 11
227 In terms of basic units of mass(M),
length(L), time(T) and charge(Q), the dimensions of magnetic permeability of
vacuum ( left(mu_{0}right) ) would be?
( mathbf{A} cdotleft[M L Q^{-2}right] )
B . ( left[L T^{-1} Q^{-1}right] )
( mathbf{c} cdotleft[M L^{2} T^{-1} Q^{-2}right] )
D ( cdotleft[L T Q^{-1}right] )
11
228 If ‘OLYMPIAD’ is the unit of a new
physical quantity. How many times more then 1 Mega OLYMPIAD when compered to ten milli OLYMPIAD?
11
229 The value of ( frac{pi}{mathbf{5 3 . 2}} ) with due regard to significant figures is (Use ( boldsymbol{pi}=mathbf{3 . 1 4} ) ) :
A .0 .0591
B. 0.0590
c. 0.590
D. 0.5906
11
230 In the relation ( frac{d y}{d x}=2 omega sin left(omega t+phi_{0}right) ) the
dimensional formula for ( omega t+phi_{0} ) is
A . MLT
в. мLт
c. мL ( ^{0} neg^{0} )
D. M^ ( ^{0} ) L ( ^{0} ) Т ( ^{0} )
11
231 Illustration 1.14 Experiments reveal that the velocity v of
water waves may depend on their wavelength 2, density of
water p, and acceleration due to gravity g. Establish a possible
relation between v and 2, 8, p.
11
232 Volume is a derived quantity of
A. Length
B. Mass
c. Density
D. Relative density
11
233 With the increase in temperature, the density of a substance, in general,
A. increases
B. decreases
c. first increase then decreases
D. first decrease then increases
11
234 The initial and final temperatures are
recorded as ( (40.6 pm 0.3)^{0} C ) and
( (50.7 pm 0.2)^{0} C . ) The rise in temperature
is:
A ( cdot 10.1^{0} C )
B ( cdot(10.1 pm 0.3)^{0} C )
c. ( (10.1 pm 0.5)^{0} C )
D. ( (10.1 pm 0.1)^{0} C )
11
235 When ( 24.25 times 10^{3} ) is rounded off to
three significant figures, it becomes:
A .242
B. 243
c. ( 244 times 10^{2} )
D. ( 24.2 times 10^{3} )
11
236 2. The dimensions of the quantities in one (or more) of the
following pairs are the same. Identify the pair(s).
a. Torque and work
b. Angular momentum and work
c. Energy and Young’s modulus
d. Light year and wavelength (IIT JEE, 1986)
raduate le dimensional formule of the pommittitur
11
237 If energy( ( E ) ), velocity ( (V) ) and force ( (F) ) be taken as fundamental quantity, then what are the dimension of mass?
A ( . E V^{2} )
B. ( E V^{-2} )
( mathbf{c} cdot F V^{-1} )
D. ( F V^{-2} )
11
238 Assertion
The value of 1 Micron is equal to ( 10^{-5} m )
Reason
Micron is the unit for measuring
microscopic distance.
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
239 In the screw gauge, the screw should be
moved in the same direction to avoid
which of the following error?
A . Zero error
B. Parallel error
c. Backlash error
D. Index error
11
240 The length of a simple pendulum is determined by measuring the length of thread / by meter scale and radius of bob r by Vernier callipers. The effective length ( L ) is obtained by adding the two i.e., ( boldsymbol{L}=boldsymbol{l}+boldsymbol{r} . ) If ( boldsymbol{l}=mathbf{1 0 2 . 4} mathrm{cm} ) and ( boldsymbol{r}= )
( 2.24 mathrm{cm}, ) how would you use quote ( L ) in proper significant figures?
( A cdot 104.64 mathrm{cm} )
B. 104.6 cm
( c .105 mathrm{cm} )
D. ( 1.0464 mathrm{cm} )
11
241 The edge of a cube is ( a=1.2 times 10^{-2} m )
Then its volume will be recorded as :
A ( cdot 1.7 times 10^{-6} m^{3} )
В. ( 1.70 times 10^{-6} m^{3} )
C. ( 1.70 times 10^{-7} m^{3} )
D. ( 1.78 times 10^{-6} m^{3} )
11
242 According to theory of significant figures the value of ( sqrt{mathbf{3 . 0}} ) is:
A. 1.732
в. 1.7
c. 1.73
D. 1.8
11
243 The length of a curved surface is
measured by using
A. metre scale only
B. thread only
c. both metre scale and thread
D. none of these
11
244 What do you mean by dynamic
spherometer?
A. An instrument used to measure radius of curvature
directly
B. An instrument used to measure radius of curvature
more accurately than usual spherometer.
C. An instrument used to measure radius of curvature indirectly
D. None of these
11
245 The wrong unit conversion among the
following is
( mathbf{A} cdot 1 ) angstrom ( =10^{-10} m )
B. 1 fermi ( =10^{-15} mathrm{m} )
C ( . ) 1 light year ( =9.46 times 10^{15} mathrm{m} )
D. 1 astronomical unit ( =1.496 times 10^{-11} mathrm{m} )
11
246 Which of the following length measurements is most precise and why?
a. ( 2.0 mathrm{cm} )
b. ( 2.00 c m )
c. ( 2.000 mathrm{cm} )
11
247 28. The error in the measurement of the radius of a sphere
is 0.5%. What is the permissible percentage error in the
measurement of its (a) surface area and (b) volume?
-LL1.
1
11
248
T
U
|
14. Which of the following measurement is most precise?
(a) 5.00 mm
(b) 5.00 cm
(c) 5.00 m
(d) 5.00 km
11
249 State, for each of the following physical quantities, if it is a scalar or a vector:
volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.
11
250 25. The radius of the earth is 6.37 x 10ºm and its mass is 5.975
x 10-4 kg. Find the earth’s average density to appropriate
significant figures.
11
251 Arrange the following physical quantities in the decreasing order of dimension of length.
I. Density
II. Pressure
III. Power
IV. Impulse
( mathbf{A} cdot ) ।, ॥, ॥ा, ।V
B. ॥II, II, I, IV
c. ( 1 mathrm{V}, ) । ॥ ( , ) ॥)
D. III, IV, II, I
11
252 Name The Sl unit of mass. 11
253 1. Force F and density d are related as F =
find the dimensions of a and B.
B+Tg, then
11
254 The radius of a hydrogen atom is ( 0.5 dot{A} ) Find the order of magnitude of volume
of 1 mole hydrogen in ( m^{3} . ) Given that 1
mole of hydrogen has ( 6.02 times 10^{23} )
hydrogen atoms.
A ( cdot 2 times 10^{-4} m^{3} )
B. ( 10^{-3} m^{3} )
( mathbf{c} cdot 10^{-7} m^{3} )
D. ( 10^{-2} m^{3} )
11
255 In SI system, the unit of work is 11
256 Explain the statement “relative density
of brass is ( 8.4 ” )
11
257 Derived units can be defined in terms of
one or two of all the fundamental units
in them.
A. True
B. False
11
258 The diameter of a cylinder is ( 0.55 mathrm{cm} ) its length is ( 1.35 mathrm{cm} . ) Its volume
is ( c m^{3} )
A . 0.3240
в. 0.32
c. 0.324
D. 3.2
11
259 The diameter of a sphere is ( 3.34 m )
Calculate its volume with due regard to significant figures.
11
260 In an experiment, the following observations were recorded:
( boldsymbol{L}=mathbf{2 . 8 2 0 m}, boldsymbol{M}=mathbf{3 . 0 0 k g}, boldsymbol{l}= )
( 0.087 c m, ) diameter ( D=0.041 c m )
Taking ( g=9.81 m s^{-2} ) and using the
formula, ( Y=frac{4 M g}{pi D^{2} l}, ) find the maximum permissible error in ( Y )
11
261 Which of the following measurement is most precise?
A. ( 5.00 mathrm{mm} )
B. ( 5.00 mathrm{cm} )
c. ( 5.00 m )
D. ( 5.00 mathrm{km} )
11
262 The velocity ‘ ( V ) ‘ of a particle varies with distance ‘ ( x ) ‘ and time ‘t’ as ( boldsymbol{V}= )
( boldsymbol{A} sin (boldsymbol{B} boldsymbol{x}) cos (boldsymbol{C} boldsymbol{t}) ) when ( boldsymbol{A}, boldsymbol{B}, boldsymbol{C} ) are
constants, then ( frac{boldsymbol{A} boldsymbol{B}}{boldsymbol{C}} ) will have the dimensions of:
A. velocity
B. acceleration
c. pressure
D. strain
11
263 If ( x, v ) and a denote the displacement, the velocity and the acceleration of a
particle executing simple harmonic motion of time period ( T, ) then which of the following do not change with time?
A ( cdot frac{a T}{v} )
В . ( a T+2 pi v )
c. ( a^{2} T^{2}+4 pi^{2} v^{2} )
D. ( a T )
E . ( v T )
11
264 Pick out the only vector quantity in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.
11
265 Choose the correct statement from the
following options.
This question has multiple correct options
A. If the zeroeth division of the vernier and main scales of
a standard vernier callipers coincide then measured length is equal to the actual length.
B. The least count of vernier scale is ( 0.9 mathrm{mm} )
C. The length of a one vernier scale division is greater than that of one main scale division.
D. The internal jaws are used for measuring the internal diameter of a hollow cylinder
11
266 The standard quantity used for comparison is called a
A. unit
B. quality
c. pick
D. coin
11
267 A point mass of ( 10 k g ) is placed at the
centre of Earth. The weight of the point mass will be
A. zero
B. Infinite
c. Less than zero
D. ( 10 k g )
11
268 Which one of the following pair of quantities has same dimension?
A. Force and work done
B. Momentum and impulse
c. Pressure and force
D. Surface tension and stress
11
269 According to Joule’s law of heating, heat produced ( boldsymbol{H}=boldsymbol{l}^{2} boldsymbol{R} boldsymbol{t}, ) where I is current
( mathrm{R} ) is resistance, and ( mathrm{t} ) is time. If the
errors in the measurement of I,R and t
are ( 3 %, 4 % ) and ( 6 %, ) respectively, find
error in the measurement of H.
11
270 Which one of the following is not a fundamental SI unit?
A. Ampere
B. Candela
c. Newton
D. Kelvin
11
271 6. If the time period (T) of vibration of a liquid drop depends
on surface tension (S), radius (r) of the drop and density
(p) of the liquid, then the expression of T is
(a) T=k/pr3/s (b) T = k/p1/2,3 15
(c) T=k/pr3/s1/2 (d) None of these
11
272 A physical quantity ( rho ) is related to four variables ( boldsymbol{alpha}, boldsymbol{beta}, boldsymbol{gamma} ) and ( boldsymbol{eta} ) as ( boldsymbol{rho}=frac{boldsymbol{alpha}^{3} boldsymbol{beta}^{2}}{sqrt{boldsymbol{gamma} boldsymbol{eta}}} ) The
percentage errors of measurements in ( boldsymbol{alpha}, boldsymbol{beta}, boldsymbol{gamma} ) and ( boldsymbol{eta} ) are ( 1 %, 3 %, 4 % ) and ( 2 % )
respectively. Find the percentage error
in ( rho )
A . 6.5%
B. 12%
c. 21%
D. 26%
11
273 What are the rules (sign conventions) to use ( S . I ) units? 11
274 How many light years Alpha Centauri away from the Earth?
A . 1.29
B. 2.29
c. 3.29
D. 4.29
11
275 Which of the following is the most
accurate instrument?
A. A scale whose least count is ( 0.1 mathrm{cm} )
B. A vernier caliper in which 10 vernier divisions coincide with 9 main scale divisions whose main scale is millimetre scale.
C. A microscope in which 50 vernier divisions coincide with 49 main scale divisions whose main scale is millimetre scale.
D. A microscope in which 50 vernier divisions coincide with 49 main scale divisions and in the main scale
there are 20 divisions in ( 1 mathrm{cm} )
11
276 If the length of the cylinder is measured as ( 25 mathrm{mm} ), the diameter is ( 3.09 mathrm{cm} ) and mass of the cylinder is measured as ( 50.0 mathrm{gm} ) find the density of the cylinder in proper significant figures.(in ( boldsymbol{g} boldsymbol{m} / boldsymbol{c m}^{3} boldsymbol{)} )
A . 2.700 ( g m / c m^{3} )
в. 2.7 ( g m / c m^{3} )
c. ( 0.27 g m / c m^{3} )
D. ( 2.70 g m / c m^{3} )
11
277 14. If P represents radiation pressure, c represents speed of
light and represents radiation energy striking a unit area
per second, then non-zero integers x, y and z such that
P’Q’C is dimensionless are
(a) x = 1, y = 1, z =-1
(b) x= 1, y=-1, z = 1
11
278 Which of the following is correct for dimensionless quantity?
A. It does not exist
B. It always has a unitt
c. It never has a unit
D. It may have a unitt
11
279 26. The dimensions of the formula of capacitance are
a. [M-‘L-2 TA?) b. [M-L TAPI
c. [M-‘L-214A?] d. [M-L2T2 A21
11
280 5. A student when discussing the properties of a medium
(except vacuum) writes
Velocity of light in vacuum = Velocity of light in
medium
This formula is
a. Dimensionally correct
b. Dimensionally incorrect
c. Numerically incorrect
d. Both a and c
11
281 30. In an experiment on the determination of Young’s Modulus
of a wire by Searle’s method, following data is available:
Normal length of the wire (L) = 110 cm
Diameter of the wire (d) = 0.01 cm
Elongation in the wire (1) = 0.125 cm
This elongation is for a tension of 50 N. The least counts
for corresponding quantities are 0.01 cm, 0.00005 cm, and
0.001 cm, respectively. Calculate the maximum error in
calculating the value of Young’s modulus (Y).
iment for determining the role of
clorotion
11
282 5
3. Let [8] denote the dimensional formula of the permittivity
of vacuum and [M] that of the permeability of vacuum. If
M=mass, L = length, T=time, and I=electric current, then
a. [x] = M’L-3721
b. [ɛ] =M’L-31412
c. [M] = MLT-21-2
d. (Mo] = ML?T-1
(IIT JEE, 1998)
11
283 The number of significant figures in
3400 is :
A . 4
B.
( c cdot 3 )
( D )
11
284 If length of a pendulum of wall clock is increased by ( 0.1 % ), then find error in time per day. 11
285 millimeter is
( mathbf{A} cdot 10^{-15} )
B ( cdot 10^{-14} )
c. ( 10^{-13} )
D. ( 10^{-16} )
11
286 Illustration 1.12 A famous relation in physics relates the
moving mass m to the rest mass m, of a particle in terms of its
speed v and the speed of light c. (This relation first arose as a
consequence of the special theory of relativity due to Albert
Einstein). A boy recalls the relation almost correctly but forgets
mo
where to put the constant c. He writes m= –
(1 – 2 1/2 . Guess
where to put the missing c.
e
13
11
287 c. y = x
do y=-x
59. A physical quantity x is cal
Calculate the percentage error in measuring x when the
percentage errors in measuring a, b, and care 4,2, and 3%,
respectively.
a. 7%
b. 9%
c. 11%
d. 9.5%
60
CV
11
288 When a symbol is used to represent a unit named after a person, lower-case letters are used.
A. True
B. False
11
289 *.
***Minum V
uru wvl Idul i al 15
16. The dimensions of universal gravitational constant are
11
290 15. The effective length of a simple pendulum is the sum of
the following three: length of string, radius of bob, and
length of hook.
In a simple pendulum experiment, the length of the string,
as measured by a meter scale, is 92.0 cm. The radius of the
bob combined with the length of the hook, as measured
by a vernier callipers, is 2.15 cm. The effective length of
the pendulum is
a. 94.1 cm
b. 94.2 cm
c. 94.15 cm
d. 94 cm
11
291 11. If force (F), length (L) and time (T) are assumed to be
fundamental units, then the dimensional formula of the
mass will be
(a) FL-T2 (6) Fl-T2 (c) Fl-11 (d) FL?T?
11
292 A physical quantity ( x ) can be dimensionally represented in terms of ( M, L ) and ( T ) is ( x=M^{a} L^{b} T^{c} . ) The
quantity time
A. may be dimensionally represented in terms of ( x, M ) and ( L ) if ( c neq 0 )
B. may be dimensionally represented in terms of ( x, M ) and ( L ) if ( c=0 )
c. may be dimensionally represented in terms of ( x, M ) and ( L ), irrespective of ( c )
D. may be dimensionally represented in terms of ( x, M ) and ( L )
11
293 ( mathrm{cm} ) make ( 3.25 mathrm{km} ) 11
294 In the formula ( X=3 Y Z^{2}, X ) and ( Z ) have
dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are
A. -2 in mass, -2 in length, 4 in time and 5 in charge.
B. – 3 in mass, – 2 in length, 4 in time and 4 in charge.
c. -4 in mass, -5 in length, 4 in time and 4 in charge.
D. -3 in mass, -2 in length, 8 in time and 7 in charge.
11
295
musu UNI!
2. A physical quantity X is related to four measurable
quantities a, b, c and d as follows X = ab3c12d. The
percentage error in the measurement of a, b, c and d are
190,2%, 3% and 4%, respectively. What is the percentage
error in quantity X? I
11
296 Consider the following pairs of quantities:
1. Young’s modulus; pressure
2. Torque; energy
3. Linear momentum; work
4. Solar day; light year In which cases are the dimensions,
within a pair, same?
A . 1 and 3
B. 1 and 4
( c cdot 1 ) and 2
D. 2 and 4
11
297 vur urut 113 Pom
14. The length and breadth of a rectangle are (5.7 + 0.1) cm
and (3.4 + 0.2) cm. Calculate the area of the rectangle
with error limits.
11
298 Velocity’ ( V^{prime} ) of a wave is directly
proportional to modulus of elasticity’ ( boldsymbol{E} ) and density ‘ ( d ) of a medium. The
expression of ‘ ( V ) ‘ using dimensional analysis is:
A ( cdot V=frac{E}{sqrt{d}} )
B. ( V=frac{sqrt{E}}{d} )
c. ( v=sqrt{frac{E}{d}} )
D. ( V=sqrt{E D} )
11
299 Which of the following statements
is/are false?
A. Mass, speed and energy are scalar quantities
B. Momentum, force and torque are vector quantities
C. Distance is a scalar quantity but displacement is a vector quantity
D. A vector has only magnitude, whereas a scalar has both magnitude and direction
11
300 A cup of water was heated for eight minutes. The thermometers show the
temperature readings during different times of heating.What can be the
temperature when it is heated for three
minutes?
( A, 2 )
в. 28
( c cdot 28 )
D. 30
11
301 The dimension of magnetic field in ( M, L, T ) and ( C ) (Coulomb) is given as:
A. ( M L T^{-1} C^{-1} )
B. ( M T^{2} C^{-2} )
c. ( M T^{-1} C^{-1} )
D. ( M L T^{-2} C^{-1} )
11
302 9. The period of oscillation of a simple pendulum in the
experiment is recorded as 2.63 s, 2.56 s, 2.42 s, 2.71 s and
2.80 s respectively. The average absolute error is
(a) 0.1 s
(b) 0.11 s
(c) 0.01 s
(d) 1.0 s
11
303 2. In the following equations, the distance x is in metres, the
time t in seconds and the velocity v in metres/second. What
are the SI units of the constants C, and Cz?
(a) v2 = 2CX
(b) x = C. cos Cat
(c) v=Ce-C21
11
304 Find the order of magnitude of length of rod having length ( left(10^{6}+10^{3}right) mathrm{m} ) 11
305 The least count of a stop watch is 0.2 second. The time of 20 oscillations of a
pendulum is measured to be 25 seconds. The percentage error in the time period is
A . ( 16 % )
B. 0.8 %
c. ( 1.8 % )
D. 8%
11
306 A student performs an experiment for determination of ( boldsymbol{g}=left[frac{mathbf{4} boldsymbol{pi}^{2} boldsymbol{L}}{boldsymbol{T}^{2}}right], boldsymbol{L}=mathbf{1} boldsymbol{m} )
and he commits an error of ( triangle L ). For The
takes the time of n oscillations with the
stopwatch of least count ( triangle T . ) For which
of the following data, the measurement of ( g ) will be most accurate?
A. ( triangle L=0.5, Delta T=0.1, n=20 )
B. ( triangle L=0.5, Delta T=0.1, n=50 )
c. ( triangle L=0.5, Delta T=0.01, n=30 )
D. ( triangle L=0.5, Delta T=0.05, n=50 )
11
307 Which one of the following methods is used to measure distance of a planet or
a star from the earth?
A. Echo method
B. Parallax method
c. Triangulation method
D. None of these
11
308 (U Suess dulu sulan
5. The dimensional formula for impulse is same as the
dimensional formula for
(a) Momentum
(b) Force
(c) Rate of change of momentum
(d) Torque
11
309 Calculate the weight of the block at a distance of four times of Earth radii
from the center of the Earth. It is given that ( g ) is the acceleration due to gravity at the surface of Earth and mass of the
block is ( mathrm{m} )
A. ( 16 mathrm{mg} )
B. ( 4 mathrm{mg} )
c. ( 2 mathrm{mg} )
D. ( frac{1}{4} mathrm{mg} )
E ( cdot frac{1}{16} mathrm{mg} )
11
310 The dimensional formula of coefficient
of viscosity is
( mathbf{A} cdotleft[M L T^{-1}right] )
B . ( left[M^{-1} L^{2} T^{-2}right] )
( mathbf{c} cdotleft[M L^{-1} T^{-1}right] )
D. none
11
311 Assertion
The given equation ( boldsymbol{x}=boldsymbol{x}_{0}+boldsymbol{u}_{0} boldsymbol{t}+ )
( frac{1}{2} a t^{2} ) is dimensionally correct, where
is the distance travelled by a particle in
time ( t, ) initial position ( x_{0}, ) initial velocity
( u_{0} ) and uniform acceleration a is along the direction of motion
Reason
Dimensional analysis can be used for checking the dimensional consistency or homogeneity of the equation.
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
312 10. In S=a+bt + ct. Sis measured in metres and t in seconds.
The unit of c is
(a) None
(b) m
(c) ms-1
(d) ms=2
11
313 A science student takes 100
observations in an experiment. Second
time he takes 500 observations in the
same experiment. By doing so the possible error becomes:
A. 5 times
B. ( 1 / 5 ) times
c. unchanged
D. none of these
11
314 A body is submerged in water. It is taken out and then submerged in mercury. What happens to its relative density with respect to the liquid in which it is submerged?
A . increases
B. decreases
c. remains constant
D. can’t say
11
315 The Sl units of mass and weight are
A. ( mathrm{kg} ) and ( mathrm{kg} )
B. N and kg
c. kg and ( mathrm{N} )
D. N and N
11
316 Assertion
In the measurement of physical quantities direct and indirect methods
are used.
Reason
The accuracy and precision of
measuring instruments along with
errors in measurements should be
taken into account, while expressing
the result.
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
317 Assertion
( 1 m m^{2}=10^{-6} m^{2} )
Reason
The numerical value of physical quantity is less for a smaller unit.
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
318 Which expression has the same SI base
units as pressure?
A. ( frac{text { force }}{text { length } times text { speed }} )
в. ( frac{text { force }}{text { length } times text { time }} )
c. ( frac{text { mass }}{text { length } times(text { time })^{2}} )
D. ( frac{text { mass } times(text { time })^{2}}{text { length }} )
11
319 The symbol for metre is written as:
A . ( m )
в. ( M )
( c cdot mu )
D. All of the above
11
320 The value of ( frac{sin 50^{circ}}{sin 30^{circ}} ) 11
321 The edge of a cube is measured using a vernier callipers. ( [9 ) divisions of the main scale is equal to 10 divisions of vernier scale and 1 main scale division
is ( 1 mathrm{mm} ) ]. The main scale division reading is 10 and 1 division of vernier scale was found to be coinciding with the main scale. The mass of the cube is
2.736 gm. Calculate the density in ( mathrm{gm} / mathrm{cm}^{3} ) up to correct significant figures.
11
322 If a conductance of a conductor (G) is ( frac{I^{2} t}{W}, ) where I is current, t is time and ( w ) is work done then write the unit of
conductance expressed in terms of fundamental units.
A. ( frac{A^{2} s^{3}}{k g} m^{2} )
в. ( frac{A^{3} s^{2}}{k g} m^{2} )
c. ( frac{A^{2} s^{3}}{k g} m^{1} )
D. ( frac{A^{3} s^{2}}{k g quad m^{1}} )
11
323 If the earth expands suddenly to twice its diameter, what would be length of
the day?
11
324 The radius ( (r), ) length ( (l) ) and resistance
( (R) ) of a thin wire are ( (0.20 pm 0.01) mathrm{cm} )
( (800 pm 0.1) mathrm{cm}, ) and ( (301 pm 1) Omega )
respectively. The error in the specific resistance is :
A . 10.34%
B . 45.4%
c. 26%
D. 27.5%
11
325 26. A man runs 100.5 m in 10.3 sec. Find his average speed
up to appropriate significant figures.
1

1
:11
11
326 Multiple Correct Answers Type The values of measurement of a
physical quantity in five trials were found to be 1.51,1.53,1.53,1.52 and
( mathbf{1 . 5 4} . ) Then
A. Average absolute error is 0.01
B. Relative error is 0.01 .
c. Percentage error is ( 0.01 % )
D. Percentage error is ( 1 % ).
11
327 A person was weighing ( 102.1 mathrm{kg} ) last
week and gained ( 0.28 k g ) this week. His
weight as of now is correctly expressed
as:
A. ( 102.38 mathrm{kg} )
в. ( 102.3 mathrm{kg} )
c. ( 102.4 mathrm{kg} )
D. ( 102 mathrm{kg} )
11
328 Measurement can be accurate without
being precise. True=1, false = 0
11
329 A star has a parallax angle ( p ) of 0.723 arcseconds. What is the distance of the
star?
A . 1.38 parsecs
B. 2.38 parsecs
c. 3.38 parsecs
D. 4.38 parsecs
11
330 Parallax is the apparent displacement of an object because of:
A. change in observer’s point of view
B. change in object’s position
c. changes both in observers point of view and object’s position
D. consistency in observer’s point of view
11
331 You have a bag of cotton and an iron bar
each indicating a mass of ( 100 k g ) when measured on a weighing machine. In reality, one is heavier than the other Can you say which one is heavier and why?
11
332 The density of water is ( 1 g m / c m^{3} . ) What is its value in SI units? 11
333 Subtract ( 1.5 times 10^{3} ) from ( 4.8 times 10^{4} ) with
due regard to significant figures.
A. ( 4.6 times 10^{4} )
B. ( 4.6 times 10^{5} )
c. ( 4.6 times 10^{6} )
D. ( 5 times 10^{4} )
11
334 41. The velocity of transverse wave in a string is v= Tim
where T is the tension in the string and m is the mass per
unit length. If T=3.0 kgf, the mass of string is 2.5 g and
the length of string is v = 1.000 m, then the percentage
error in the measurement of velocity is
a. 0.5 . b. 0.
7 c . 2.3 d. 3.6
11
335 Choose the correct statement from the
following
This question has multiple correct options
A. Distance between earth and nearest star is of order in
parsec.
B. Thousand millimetre make one metre.
C. 1 tonne is equal to ( 10^{6} ) g.
D. A simple pendulum is used to measure the mass of a bob
11
336 Illustration 1.1 Convert Newton into dyne. 11
337 What is a lunar month?
A. month having 29 days
B. a lunar month is the time between two identical syzgies (new moons or full moons)
C. Moon’s orbital period in a non-rotating frame of reference
D. average time for the Moon to pass twice through the same equinox point of the sky
11
338 Measuring vessel to measure density of
liquid is
11
339 Match the physical quantities given in Column I with suitable dimensions
expressed in Column II.
II Column I ( quad ) Column
a) Angular momentum
1) ( M^{-1} L^{3} T^{-2} )
b) Torque
2) ( M L T^{-2} )
c) Gravitational constant
3) ( M L^{2} T^{-2} )
d) Tension
4) ( M L^{2} T^{-1} )
A. a-1, b-3, c-4, d-2
B. a-1, b-4, c-3 d-2
c. ( a-4, b-3, c-1, d-2 )
D. a-1, b-2, c-4, d-3
11
340 The method of dimensional analysis
can be used to derive which of the
following relations?
A. ( N_{0} e^{-lambda} )
B. ( operatorname{Asin}(omega+k x) )
c. ( frac{1}{2} m v^{2}+frac{1}{2} omega^{2} )
D. None of these
11
341 Zepto ( =10^{-x}, ) then ( x ) is ? 11
342 In a practical unit if the unit of mass
becomes double and that of u it of time
becomes half, then 8 joules will equal to unit of work
( A cdot 8 )
B. 4
( c )
D. 10
11
343 Three successive measurement in an
experiment gave value 10.9,11.4042 and 11.42 the correct way of reporting the average value is:
11
344 ‘The order of magnitude of a physical quantity must be expressed in proper unit’. Comment on this statement 11
345 If ( m ) is the mass of drop of a liquid of radius ( r, ) then ( frac{m g}{pi r} ) has the same dimensions of :
A. Surface tension
B. Tension
c. Young’s Modulus
D. coefficient of viscosity
11
346 Newton is written in fundamental units
( operatorname{as} k g m / s^{x} . ) Value of ( x ) is:
( A cdot 2 )
B. 3
( c cdot 1 )
( D cdot-2 )
11
347 Fill in the blanks with the correct words:
The distance of an object from one end
to the other is called
(length/kilometer)
11
348 Name the three convenient units used
to measure length ranging from very short to very long value. How are they related to the S.I. unit?
11
349 Area of a square is ( (100 pm 2) m^{2} . ) Its
side is:
A. ( (10 pm 1) m )
в. ( (10 pm 0.1) m )
c. ( (10 pm sqrt{2}) m )
D. ( 10 pm sqrt{2} % )
11
350 If force ( F, ) acceleration ( a, ) and time ( T )
are taken as the fundamental physical quantities, the dimensions of length on
this system of units are
( mathbf{A} cdot F A T^{2} )
в. ( F A T )
c. ( F T )
D. ( A T^{2} )
11
351 U
125%
13. A physical quantity A is related to four observable a, b,
0253
c and d as follows, A=” , the percentage errors of
. Cvd .
measurement in a, b, c and d are 1%, 3%, 2% and 2%
respectively. What is the percentage error in the quantity
A?
(a) 12% (b) 7% (c) 5% (d) 14%
11
352 Count total number of S.F. in 5.003020
( A cdot 3 )
B. 20
( c .7 )
D.
11
353 What is the mass of an object whose weight is ( 98 mathrm{N} ? )
A. ( 98 mathrm{kg} )
B. ( 9.8 mathrm{kg} )
( c cdot 10 mathrm{kg} )
D. none of these
11
354 Order of ( frac{1}{8 times 10^{9}} ) is:
( mathbf{A} cdot 1.77 times 10^{-10} )
B ( .1 .25 times 10^{-10} )
C ( .1 .55 times 10^{-10} )
D. ( 1.95 times 10^{-10} )
11
355 Which of the following is used as ( mathrm{S} ) I prefixes:
A . Micro
B. Mica
c. Mikro
D. Maca
11
356 Sl unit of weight is kilogram-force ( (K g f )
).
A. True
B. False
11
357 The physical quantity can be expressed
as
11
358 A cube has a side of length ( 1.2 times )
( 10^{-2} m . ) Calculate its volume
A ( .1 .7 times 10^{-6} m^{3} )
В. ( 1.73 times 10^{-6} m^{3} )
C. ( 1.70 times 10^{-6} m^{3} )
D. ( 1.728 times 10^{-6} mathrm{m}^{3} )
11
359 The least count of a stop watch is 0.2 second.The time of 20 oscillations of a
pendulum is measured to be 25 seconds.The percentage error in time period is
A . 16%
в. 0.8%
c. ( 1.8 % )
D. 8%
11
360 The dimension of angular momentum is
( mathbf{A} cdotleft[M^{0} L^{1} T^{-1}right] )
B . ( left[M^{1} L^{2} T^{-2}right] )
C ( cdotleft[M^{1} L^{2} T^{-1}right] )
D cdot ( left[M^{2} L^{1} T^{-2}right] )
11
361 Sl unit of heat capacity is
A. joule
B. joule/kilogram
C . joule/(kilogram x kelvin)
D. joule/kelvin
11
362 light year = – 11
363 The number of significant figures in
0.010200 is :
A. 6
B. 5
( c cdot 4 )
( D )
11
364 Density of a solid is ( 18300 k g / m^{3} . ) What
is its relative density?
A. 1830
B. 183
( c cdot 18.3 )
D. 1.83
11
365 (d) 5.0 x IU
curacy of measurement and significant
sing results of experiment, which of the
leasurements 50.14 cm and 0.00025
10. In the context of accuracy of measure
figures in expressing results of ex
following is/are correct
(1) Out of the two measurements 50.14
ampere, the first one has greater accuracy
(2) If one travels 478 km by rail and 397 mby
total distance travelled is 478 km.
(a) Only (1) is correct (b) Only (2) is correct
(c) Both are correct (d) None of them is correct
0 km by rail and 397 m by road, the
11
366 13. The sides of a rectangle are (10.5 + 0.2) cm and (5.2,
0.1) cm. Calculate its perimeter with error limits.
11
367 12. A watt is:
(a) kg m/s2
(c) kg m/s
(b) kg m-/s3
(d) kg m?/s2
11
368 The Van der Wall equation for 1 mole of a real gas is ( left(boldsymbol{P}+frac{boldsymbol{a}}{boldsymbol{V}^{2}}right)(boldsymbol{V}-boldsymbol{b})=boldsymbol{R} boldsymbol{T} )
where ( P ) is the pressure, ( V ) is the
volume, ( boldsymbol{T} ) is the absolute temperature ( R ) is the molar gas constant and ( a, b ) are Van der Wall constants. The dimensions
of ( a ) are the same as those of :
A . ( P V )
в. ( P V^{2} )
c. ( P^{2} V )
D. ( P / V )
11
369 What is dimensional formula for
magnetic flux densities?
11
370 Two numbers are given as i) 20.96 and
ii) ( 0.0003125 . ) Rounding off above numbers to 3 significant figures will lead to :
A ( . ) i) ( 21.0, ) ii) 312
B . i) 21.0, ii) 3.12 ( times 10^{-4} )
( c cdot ) i) ( 2.10, ) ii) ( 3.12 times 10^{-4} )
4
4
11
371 Which of these is not a base quantity in mechanics?
A. Charge
B. Length
c. Mass
D. Time
11
372 12. Position of a body with acceleration ‘a’ is given by x =
Ka”t”, here t is time. Find dimension of m and n.
(a) m= 1, n=1 (b) m= 1, n = 2
(c) m =2, n=1
(d) m = 2, n=2
11
373 The value of Faraday number in Sl unit
is:
A. 9.65 coulomb ( / mathrm{kg} ) – equivalent
B . ( 9.65 times 10^{7} ) coulomb ( / mathrm{kg} ) – equivalent
c. ( 9.65 times 10^{-7} ) coulomb / ( k g ) – equivalent
D. 9.65 coulomb ( / g ) – equivalent
11
374 Quantity of matter contained in a body
is
A. Mass
B. density
c. relative density
D. volume
11
375 gigameter is ( 10^{-a} ) exameter. What is
value of a?
11
376 Illustration 1.32 If the measured value of
R= 1.05 12, wire diameter d = 0.60 mm, and length
cm, then find the maximum permissible error in resistivity,
R(id-14)
= 0.60 mm, and length 1 = 75.3
p=
11
377 The effective length of a simple pendulum is the sum of the following three: length of string, radius of bob, and length of hook. In a simple pendulum experiment, the length of the string, as measured by a meter scale, is ( 92.0 mathrm{cm} . ) The radius of
the bob combined with the length of the hook, as measured by a vernier
callipers, is ( 2.15 mathrm{cm} . ) The effective length of the pendulum is
( mathbf{A} cdot 94.1 mathrm{cm} )
B. ( 94.2 mathrm{cm} )
c. ( 94.15 mathrm{cm} )
D. ( 94 mathrm{cm} )
11
378 Illustration 1.21 The relative density of material of a body
is found by weighing it first in air and then in water. If the
weight in air is (5.00+ 0.05) N and the weight in water is
(4.00 +0.05) N. Find the relative density along with the
maximum permissible percentage error.
11
379 According to theory of significant
figures ( (2.0)^{10} ) is :
A ( cdot 1024 )
В. ( 1.024 times 10^{10} )
c. ( 1.0 times 10^{3} )
D. 1000
11
380 A thin wire has a length of ( 21.7 mathrm{cm} ) and
radius 0.46 mm. The volume of the wire
to correct significant figures is :
A ( .1 .4 mathrm{cm}^{3} )
B. ( 0.14 mathrm{cm}^{3} )
c. ( 0.14 mathrm{mm}^{3} )
D. None of these
11
381 11. Which one of the following does not have the same
dimensions?
(a) Work and energy
(b) Angle and strain
(c) Relative density and refractive index
(d) Planck constant and energy
11
382 4. Newton-second is the unit of
(a) Velocity
(b) Angular momentum
(c) Momentum
(d) Energy
11
383 is used as a unit to measure
the capacity of something.
A. Kilogram
B. Litre
c. Metre
D. None
11
384 The dimensions of electromotive force
in terms of current A are
( mathbf{A} cdotleft[M T^{-2} A^{-2}right] )
B . ( left[M L^{2} T^{-2} A^{2}right] )
( mathrm{c} cdotleft[M L^{2} T^{-2} A^{-2}right. )
D ( cdotleft[M L^{2} T^{-3} A^{-1}right] )
11
385 State whether True or False, and correct
the statements if false:
(1) Kilometre is a multiple of metre.
A. True
B. False
11
386 DO MILIC. ML TU. MLT
4. A physical quantity depends upon five factors, all of which
have dimensions, then method of dimensional analysis
a. Can be applied
b. Cannot be applied
c. Depends upon factors involved
d. Both (a) and (c)
11
387 If force ( F, ) work ( W ) and velocity ( v ) are
taken as fundamental quantities, then the dimensional formula of time is :
11
388 The correct way to represent an unit amount of force is :
A. 1 newton
B. 1 Newton
c. 1 NEWTON
D. None of these
11
389 The dimensional formula of a physical quantity is ( M^{1} L^{2} T^{3} I^{-1} ).What is its ( S )
unit?
A ( cdot k g quad m^{2} s^{3} A^{-1} )
B. ( k g quad m^{2} s^{2} A )
c. ( k g quad m s^{-3} A^{2} )
D. ( k g^{2} m^{2} s^{3} A^{-1} )
11
390 if ( L=2.331 c m, B=2.1 c m, ) then ( L+B= )
A. ( 4.431 mathrm{cm} )
в. ( 4.43 mathrm{cm} )
c. ( 4.5 mathrm{cm} )
D. ( 4.2 mathrm{cm} )
11
391 Identify the derived quantities among the following. This question has multiple correct options
A. Gravitational constant
B. Frequency
c. Electric charge
D. Electric current
11
392 1. Porous rock through which groundwater can move is called
an aquifer. The volume V of water that, in time t, moves
through a cross section of area A of the aquifer is given by
Vlt = KAHIL, where H is the vertical height of the aquifer
over the horizontal distance L. This relation is called
Darcy’s law. The quantity K is the hydraulic conductivity
of the aquifer. What are the SI units of K?
11
393 Repeated observations in an experiment gave the values 1.29,1.33,1.34,1.35,1.32,1.36,1.30
and ( 1.33 . ) Calculate the mean value,
absolute error, relative error, and
percentage error
11
394 The number of significant figures in
( mathbf{0 . 0 0 2 1 0} ) is
A . five
B. six
c. four
D. three
11
395 Show dimensionally that the frequency
(a) of transverse wanes in a string of
length / and mass per unit length ( boldsymbol{m} )
under a tension T is given by, ( boldsymbol{n}= ) ( boldsymbol{k} sqrt{boldsymbol{T}} / boldsymbol{l} sqrt{boldsymbol{m}} )
11
396 The dimension of permittivity of
vacuum
B ( cdotleft[M^{-1} L^{-3} T^{4} A^{3}right] )
( mathbf{c} cdotleft[M^{-1} L^{-3} T^{4} A^{2}right] )
( mathbf{D} cdotleft[M^{-1} L^{-5} T^{4} A^{2}right] )
11
397 (
101
5. Which of the following is smallest unit?
(a) Millimetre
(b) Angstrom
(c) Fermi
(d) Metre
W
: o
.f
l
f.11.
11
398 The mass and density of a solid are
measured to be ( (12.4 pm 0.1) mathrm{kg} ) and
( (4.6 pm 0.2) k g / m^{3} . ) Calculate the
volume of the sphere with error limits.
( mathbf{A} cdot therefore V pm Delta V=(2.7 pm 0.14) m^{3} )
B ( ldots V pm Delta V=(5.4 pm 0.14) m^{3} )
( mathbf{c} cdot therefore V pm Delta V=(2.7 pm 0.28) m^{3} )
D. None of these
11
399 Which of the following instrument can
be used to determine the radius of
curvature of a spherical surface?
A. Spherometer
B. Vernier callipers
c. screw gauge
D. simple pendulum
11
400 8. A physical quantity is measured and its value is found to
be nu where n=numerical value and u= unit. Then which
of the following relations is true
(a) no u
(b) no u
(c) na Vu
(d) noc –
11
401 13. Experiment shows that two perfectly neutral parallel metal
plates separated by a small distance d attract each other via
a very weak force, known as the Casimir force. The force
per unit area of the plates, F, depends only on the Planck
constant h, on the speed of light c, and on d. Which of the
following has the best chance of being correct for F?
(a) F= he
(b) F= he
(C) F = hd
(d) F = d.
(
11
402 Why are shields made of iron usually provided around precision instruments?
A. For protection against the effect of moisture in the air
B. For guiding the instruments against unauthorised handling
c. For protection against the effect of external magnetic fields
D. For absorbing heat generated during the functioning of the instruments
11
403 What is the approximation made in
the parallax method?
A. All distances measured between two points on earth is zero
B. All distances measured between two points on earth is constant
c. Distance between a point on the earth and the planet is very large as compared to the distance between two points on earth’s surface.
D. No approximation is made
11
404 Which of the following unit is not a fundamental unit:
A . Meter
B. Litre
c. second
D. Kilogram
11
405 The physical quantity which has the
dimensional formula ( left[M T^{-3}right] ) is:
A. Surface tension
c. Solar constant
D. compressibility
11
406 A length is measured as ( 7.60 mathrm{m} ). This is
the same as
A. ( 760 mathrm{mm} )
B. ( 0.0076 mathrm{mm} )
( c .760 mathrm{cm} )
D. ( 0.76 d m )
11
407 Which of the following does not has fundamental unit?
A. Mass
B. Time
c. Force
D. length
11
408 The potential energy of a particle varies
with height ( h ) from a fixed point as ( boldsymbol{E}= ) ( left(frac{boldsymbol{P} sqrt{boldsymbol{h}}}{boldsymbol{h}+boldsymbol{Q}}right) ) where, ( boldsymbol{P} ) and ( boldsymbol{Q} ) are
constants. The dimensions of ( P Q ) are
A ( cdotleft[M L^{2} T^{-2}right] )
B. ( left[M^{3 / 2} L^{3 / 2} T^{-2}right. )
C . ( left[M L^{7 / 2} T^{-2}right] )
D cdot ( left[M L^{3 / 2} T^{-2}right. )
11
409 The ratio of dimensions electric field
and magnetic field is,
A ( . M T^{1} L^{-1} )
B. ( M T^{-1} L^{-2} )
( mathbf{c} cdot M T^{2} L^{-1} )
D. ( L T^{-1} )
11
410 Temperature can be expressed as a
derived quantity in terms of :
A. length and mass
B. mass and time
c. length, mass and time
D. none of these
11
411 To convert ( ^{o} mathrm{F} ) to ( ^{circ} mathrm{C} ) formula we use, is
A ( cdot(F-32) times frac{5}{12} )
B ( cdotleft(F times frac{5}{9}right)-32 )
c. ( (F-32) times frac{9}{5} )
D. ( (F-32) times frac{5}{9} )
11
412 Surface tension of liquid is 70
dyne/cm. Its value in Sl unit is
A . ( 70 mathrm{N} / mathrm{m} )
В. ( 7 times 10^{-2} N / m )
C. ( 7 times 10^{2} N / m )
D. ( 7 times 10^{3} N / m )
11
413 2. In two systems of relations among velocity, acceleration,
02
and force are, respectively, v2 = 2 V, az = aßay, and
B1
F27
· If a and B are constants, then make relations
o laneth and time in two systems
11
414 Taking force,length and time to be the fundamental quantities.Find the direction, density,momentum and
energy
11
415 If the density of earth increases by ( 20 % ) and radius decreases by ( 20 % ) then the new value of “g” on the surface of earth will be:
A. ( 0.8 mathrm{g} )
B. ( 0.90 mathrm{g} )
c. ( 0.96 mathrm{g} )
D.
11
416 Dimensions ( left[M L^{-1} T^{-1}right] ) are related to
A. Torque
B. Work
c. Energy
D. coefficient of viscosity
11
417 24. The dimensional formula for magnetising field H is
a. IML
T
. IM LT-3A
c. MLTA-1
d. [M®LTAJ
11
418 14. A wire has a mass 0.3 + 0.003 g, radius 0.5 + 0.005 mm
and length 6 + 0.06 cm. The maximum percentage error
in the measurement of its density is
(a) 1 (6) 2 (c) 3 . (d) 4
11
419 The extent to which a given measurement agrees with the standard value for that measurement is known
as :
A. Accuracy
B. Precision
c. Accuracy and Precision
D. None of these
11
420 1. The dimensions of (1/2) EP (Ep is permittivity of free
space, E is electric field) are
a. MLT-1
b. ML27-2
c. ML-11-2
d. MLT-1
(IIT JEE, 2000)
11
421 If the unit of power is 1 million erg per minute, the unit of force is 1000 dyne and that of time is ( frac{1}{10} s, ) the unit of mass in the new system is :
( A cdot 6 g )
B. 60 g
c. ( 106 g )
D. 18
11
422 Distance travelled by sound in year is called AU?
A . True
B. False
11
423 Density of a body depends on its shape and size. True or false.
A . True
B. False
11
424 Illustration 1.16 If velocity (V), force (F), and time (T) are
chosen as fundamental quantities, express (a) mass and (b)
energy in terms of V, F, and T.
ham
11
425 Which of the following quantities is scalar?
A. Dipole moment
B. Electric force
c. Electric field intensity
D. Electric potential
11
426 The Sl unit of radioactivity is :
A . Becquerrel
B. Curie
c. Rutherford
D. None of these
11
427 Match the Column I with Column II
Column n II
nion Column
I
(Units) (Dimensional formulae)
(A) Pas Pas
( (p) )
( left[M^{0} L^{2} T^{-2} K^{-1}right] )
(B) ( mathrm{Nm} mathrm{K}^{-1} )
( (q) )
( left[M L T^{-3} K^{-1}right] )
( (C) )
( mathrm{J} mathrm{kg}^{-1} mathrm{K} )
-1
( (r) )
( left[M L^{-1} T^{-1}right] ) ”
(D) ( mathrm{W} mathrm{m}^{-1} )
( mathrm{K}^{-1} )
(s) ( left[M L^{2} T^{-2} K^{-1}right] )
( A cdot A-q, B-p, C-r, D-s )
B. ( A-p, B-q, C-s, D-r )
C. ( A-r, B-s, C-p, D-q )
D. ( A-s, B-r, C-q, D-p )
11
428 The Van der Waal’s equation of state for some gases can be expressed as:
( left(boldsymbol{P}+frac{boldsymbol{a}}{boldsymbol{V}^{2}}right)(boldsymbol{V}-boldsymbol{b})=boldsymbol{R} boldsymbol{T} )
where ( P ) is the pressure, ( V ) is the molar volume, and ( T ) is the absolute
temperature of the given sample of gas and ( a, b ) and ( R ) are constants.

In the above problem, the dimensional formula for ( mathrm{RT} ) is same as that of
A. Energy
B. Force
c. specific heat
D. Latent heat

11
429 State the requirements of a good unit. 11
430 The dimensions of energy per unit volumes are the same as those of :
A. work
B. Stress
c. Pressure
D. Modulus
11
431 7. The numbers 2.745 and 2.735 on rounding off to 3
significant figures will give
(a) 2.75 and 2.74 (b) 2.74 and 2.73
(c) 2.75 and 2.73 (d) 2.74 and 2.74
11
432 If ( mu ) is the permeability and ( epsilon ) is the permittivity then ( frac{1}{sqrt{mu epsilon}} ) is equal to
A. speed of sound
B. speed of light in vacuum
c. speed of sound in medium
D. speed of light in medium
11
433 10. The unit of potential energy is
(a) g(cm/sec2) (b) g(cm/sec)2
(c) g(cm²/sec) (d) g(cm/sec)
11
434 In the relation ( y=r sin (omega t-k x), ) the
dimensions of ( omega / k ) are
( mathbf{A} cdotleft[M^{0} L^{0} T^{0}right] )
B . ( left[M^{0} L^{1} T^{-1}right] )
( mathbf{c} cdotleft[M^{0} L^{0} T^{1}right] )
( mathbf{D} cdotleft[M^{0} L^{1} T^{0}right] )
11
435 A cube has a side of length ( 1.2 times )
( 10^{-2} m . ) Calculate its volume.
A ( .1 .7 times 10^{-6} m^{3} )
В. ( 1.73 times 10^{-6} m^{3} )
D. ( 1.732 times 10^{-6} m^{3} )
11
436 2. If velocity v, acceleration A and force F are chosen as
fundamental quantities, then the dimensional formula of
angular momentum in terms of v, A and F would be
(a) FA-‘y (b) Fv3A-2 (c) Fv2A-1 (d) F²v2A-
11
437 The dimensional formula ( M^{-1} L^{3} T^{-2} )
refers to:
A . Force
B. Power
c. Gravitational constant
D. Energy
11
438 The displacement of a body at a particular second ( n ) is given by the expression ( S_{n^{t h}}=u+frac{a}{2}(2 n-1) . ) The
dimensional formula of ( S_{n^{t h}} ) in this
equation is
( mathbf{A} cdotleft[M^{2} L^{0} T^{1}right] )
B ( cdotleft[M^{0} L^{1} T^{0}right] )
( mathbf{c} cdotleft[M^{0} L^{1} T^{-1}right] )
( mathbf{D} cdotleft[M^{0} L^{0} T^{0}right] )
11
439 The radius of sphere is measured as
then the percentage error in volume of the balls is
11
440 Which of the following is non-metric unit of length?
A . feet
B. yards
c. miles
D. all of the above
11
441 A cuboid has volume ( boldsymbol{V}=mathbf{1} times mathbf{2 l} times mathbf{3 l} )
where 1 is the length of one side. If the
relative percentage error in the
measurement of ( l ) is ( 1 % ), then the
relative percentage error in measurement of ( V ) is
( mathbf{A} cdot 18 % )
B. ( 6 % )
c. ( 3 % )
D. 1%
11
442 The density of water is equal to:
A ( cdot 10^{-3} operatorname{kg} m^{-3} )
B . ( 10^{-2} mathrm{kgm}^{-3} )
c. ( 10^{2} mathrm{kgm}^{-3} )
D. ( 10^{3} k g m^{-3} )
11
443 4. Young’s modulus of a material has the same units as
(a) Pressure
(b) Strain
(c) Compressibility (d) Force
1.1
fm 11
ingin omallest unit?
11
444 The end error of a meter bridge can be generated due to which of the following causes/(s)
A. Generation of heat due to the flow of current in the wirce may change the length of the wire
B. Due to the change of the weather, the length of the meter bridge wire may change its length.
c. The meter bridge wire is mounted over the wooden plary some metal screw or some metal
D. The thickness of the wire may be non uniform.
11
445 One astronomical unit is the mean
distance between the centre of the
Earth and centre of the
¡) Moon
ii) Sun
iii) Mars
11
446 A physical quantity ( x ) can be dimensionally represented in terms of ( M, L ) and ( T ) that is ( x=M^{a} L^{b} T^{c} . ) The
quantity time
A. may be dimensionally represented in terms of ( x, M ) and ( L ) if ( c neq 0 )
B. may be dimensionally represented in terms of ( x, M ) and ( L ) if ( c=0 )
c. may be dimensionally represented in terms of ( x, M ) and ( L ), irrespective of value of ( c )
D. can never be dimensionally represented in terms of ( x, M ) and ( L )
11
447 Calculate focal length of a spherical mirror from the following observations.
Object distance, ( boldsymbol{u}=(mathbf{5 0 . 1} pm mathbf{0 . 5}) mathrm{cm} )
and image distance, ( boldsymbol{v}=(mathbf{2 0 . 1} pm mathbf{0 . 2}) )
( mathrm{cm} )
( mathbf{A} cdot f=(14.3 pm 0.2) mathrm{mm} )
B . ( f=(14.3 pm 0.2) mathrm{cm} )
C ( cdot f=(14.3 pm 0.4) mathrm{cm} )
D. None of these
11
448 A body has a relative density of ( x ) with
respect to water at ( 25^{circ} mathrm{C} ). What is the
effect on the relative density of the body
with respect to water at ( 50^{circ} mathrm{C} ? )
A. It increases
B. It decreases
c. No effect.
D. Depends on the time of heating
11
449 If the mass of a body is ( 12.1 g ) and the
density is ( 2.2 g / c c, ) its volume is
( mathbf{A} cdot 5.5 mathrm{cm}^{3} )
в. ( 8 c c )
( c .11 c c )
D. ( 55 c c )
11
450 If the angular distance between the
stars turns out to be approximately 1100
arcseconds, or 0.30 degrees. The moon
appears to shift 0.3 degrees when we
observe it from two vantage points 2360
( mathrm{km} ) apart, then find the distance of the
moon from the surface of the
earth.Given angular diameter of moon
is 0.5 degrees.
A. ( 450642 mathrm{km} )
B. 450392 km
( c .325684 mathrm{km} )
D. ( 480264 mathrm{km} )
11
451 The centripetal force ( boldsymbol{F} ) acting on a particle moving uniformly in a circle may depend upon mass ( (boldsymbol{m}), ) velocity
( (v) ) and radius ( (r) ) of the circle. Derive
the formula for ( boldsymbol{F} ) using the method of dimensions.
( left.^{mathrm{A}} cdot_{F}=frac{m v^{2}}{r} text { (where } k=1right) )
B . ( F=m v^{2} times r ) (where ( k=1 ) )
C ( cdot F=m v^{3} times r ) (where ( k=1 ) )
D. ( F=frac{m v^{3}}{r} ) (where ( k=1 ) )
11
452 The radius of sphere is measured to be
( (2.1 pm 0.5) mathrm{cm} )
Calculate its surface area with error
limits.
( mathbf{A} cdot S=(55.4 pm 26.4) mathrm{cm}^{2} )
B . ( S=(55.4 pm 26.4) mathrm{mm}^{2} )
( mathbf{c} cdot S=(55.4 pm 13.2) mathrm{cm}^{2} )
D. None of these
11
453 Thickness of the page on which you are writing is in the order of :
A . ( 0.1 mathrm{cm} )
B. 0.1 micrometer
c. 0.1 angstrom
D. ( 0.1 mathrm{mm} )
11
454 What is the unit of relative density?
A. ( g c m^{-3} )
B. ( k g m^{-3} )
c. ( m^{3} k g^{-1} )
D. no unit
11
455 Multiple Correct Answers Type Which of the following pairs have the
same dimensions?
This question has multiple correct options
A. ( h / e ) and magnetic flux
B. ( h / e ) and electric flux
C . Electric flux and ( a / epsilon_{6} )
D. Electric flux and ( mu_{0} I )
11
456 A physical quantity is measured and the result is expressed as ( n u ) where ( u ) is
the unit used and ( n ) is the numerical
value. If the result is expressed in
various units then
A ( . n propto ) size of ( u )
В . ( n propto u^{2} )
c. ( n propto sqrt{u} )
D. ( n propto frac{1}{u} )
11
457 Which of the following is the right way of expressing 1 watt of power?
A. 1 watt
B. ( 1 mathrm{w} )
( c cdot 1 w )
D. 1 wt
11
458 The accuracy of measurement also lies in the way the result is expressed. The number of digits to which a value is to be expressed is one digit more than number of sure numbers. Rules do exist
to deal with number of digits after an operation is carried out on the given values. The error can be minimised by
many trials and using the correct methods and instruments.
The number of significant figures can reduces in
A. Addition
B. Subtraction
C. Multiplication
D. Division
11
459 Which of the following is not a unit of time?
A. hour
B. nano second
c. ( mu ) second
D. light year
11
460 A physical quantity P is given by ( boldsymbol{P}= ) ( frac{A^{3} B^{1 / 2}}{C^{-4} D^{3 / 2}} . ) Which quantity among ( A, B, C )
and D brings in the maximum percentage error in P?
11
461 A jeweller kept a diamond of mass ( 5.42 g m ) inside a box of mass ( .12 k g ) Find the combined mass of diamond
and box upto appropriate significant figures.
11
462 Which of the following is not the unit of time?
A. Leap year
B. Lunar month
c. Solar day
D. Parallactic second
11
463 Dimensional formula for Angular
momentum is:
A ( cdot M L^{2} T^{-1} )
B . ( M^{1} L^{3} T^{-1} )
c. ( M^{1} L^{1} T^{-1} )
D. ( M L^{3} T^{-2} )
11
464 The length, breadth and thickness of a
rectangular lamina are ( 1.024 m, 0.56 m )
and 0.0031 m. The volume, in ( m^{3}, ) is:
A ( .1 .8 times 10^{-3} )
В. ( 1.80 times 10^{-3} )
c. ( 0.180 times 10^{-4} )
D. 0.00177
11
465 Illustration 1.13 For a particle to move in a circular orbit
uniformly, centripetal force is required which infact depends
upon mass (m), velocity (v), and radius (r) of the circle.
Express centripetal force in terms of these quantities.
11
466 Which of the following is not used as SI prefixes:
A. Deca
B. Kilo
c. Femto
D. Mica
11
467 Define density and relative density. 11
468 Match the physical quantities given in
column A to their Sl units given in
column B:
11
469 42. Write the dimensions of alb in the relation P=4
bx
where P is the pressure, x is the distance, and t is the
time.
a. M-LºT-2
b. MLºT-2
c. MLºT
d. MLT-2
b-x²
11
470 Size of atom is measured in 11
471 A scientist performs an experiment and takes 100 readings. He repeats the same experiment and now takes 400 readings. By doing so :
A. the probable error remains the same
B. the probable error is halvedd
c. the probable error is doubled
D. the probable error reduces by a factor of ( 1 / 4 )
11
472 Disul yum uu wavelengu
2. Which of the following pairs have different dimensions!
a. Frequency and angular velocity.
b. Tension and surface tension.
c. Density and energy density.
d. Linear momentum and angular momentum.
11
473 The velocity ( v ) of sound can be assumed
as dependent on density of medium and modulus of elasticity of medium ,so which of the following can be considered as correct formula for
calculating velocity of sound, ( (rho ) =density, ( E ) =modulus of elasticity
( mathbf{A} cdot v=rho^{0.5} times E^{0.5} )
В . ( v=rho^{0.5} times E^{-0.5} )
C ( cdot v=rho^{-0.5} times E^{0.5} )
D. none of the above
11
474 Which of the following is the most
precise measurement?
A. ( 3 times 10^{-3} mathrm{m} )
B . ( 0.0030 m )
c. ( 30 times 10^{-4} mathrm{m} )
D. ( 300 times 10^{-5} mathrm{m} )
11
475 The dimensions of ( frac{alpha}{beta} ) in the equation ( boldsymbol{F}=frac{boldsymbol{alpha}-boldsymbol{t}^{2}}{beta boldsymbol{v}^{2}}, ) where ( boldsymbol{F} ) is force, ( boldsymbol{v} ) is
velocity and ( t ) is time, is :
( mathbf{A} cdotleft[M L T^{-1}right] )
B . ( left[M L^{-1} T^{-2}right] )
( mathbf{c} cdotleft[M L^{3} T^{-4}right] )
( mathbf{D} cdotleft[M L^{2} T^{-4}right] )
11
476 Assertion
nm is not same as mN
Reason
( ln m=10^{-9} m operatorname{and} 1 m N=10^{-3} N )
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
477 Dimensional formula of ( Delta Q, ) heat
supplied to the system is
( mathbf{A} cdotleft[M L^{2} T^{-2}right] )
B. ( left[M L T^{-2}right] )
( mathbf{c} cdotleft[M L^{2} T^{-1}right] )
D . ( left[M L T^{1}right. )
11
478 Write 2760000 in scientific form. 11
479 The period of oscillation of a simple pendulum in the experiment is recorded as ( 2.63 s, 2.56 s, 2.42 s, 2.71 s ) and ( 2.80 s )
respectively. The average absolute error is:
A . ( 0.1 mathrm{s} )
B. 0.11s
( c cdot 0.01 )
D. 1.0s
11
480 The number of significant figures in the
numbers ( 4.8000 times 10^{4} ) and 48000.50
are respectively
A . 5 and 6
B. 5 and 7
( c cdot 2 ) and 7
D. 2 and 6
11
481 The least count of a stop-watch is
( (1 / 5) s . ) The time of 20 oscillations of a pendulum is measured to be 25 s. What is the maximum percentage error in this measurement?
( A cdot 8 % )
B. 1%
c. ( 4 % )
D. ( 16 % )
11
482 Thickness of a pencil measured by using a screw gauge (least count. ( 001 mathrm{cm} ) ) comes out to be ( 0.802 mathrm{cm} ). The
percentage error in the measurement is
A . ( 0.125 % )
B . ( 2.43 % )
c. ( 4.12 % )
D. 2.14%
11
483 Match the columns:
( begin{array}{ll}text { । } & text { II } \ text { 1. Mass } & text { a. } m / s^{2} \ text { 2. Weight } & text { b. kilogram } \ text { 3. Gravitational acceleration } & text { c. } N m^{2} k g^{-2} \ text {4. Gravitational constant } & text { d. Newton }end{array} )
A. ( 1-a, 2-b, 3-c, 4-d )
B. ( 1-b, 2-a, 3-d, 4-c )
c. ( 1-b, 2-d, 3-c, 4-a )
D. ( 1-b, 2-d, 3-a, 4-c )
11
484 Count total number of S.F. in ( 6.020 times )
( 10^{23} )
11
485 When the planet Jupiter is at a distance
of 824.7 million kilometers from the
Earth,its angular diameter is measured to be 35.72 of arc. Calculate the
diameter of Jupiter.
11
486 6. The unit of angular acceleration in the SI system is
(a) N kg
(c) rad s-2
(d) m kg ‘K
(b) m s-2
11
487 2. The percentage errors in the measurement of mass and
speed are 2% and 3% respectively. How much will be the
maximum error in the estimation of the kinetic energy
obtained by measuring mass and speed
(a) 11% (b) 8% (c) 5% (d) 1%
1
tc… fanhanaia 101. Tha
11
488 Illustration 1.31 In resonance tube experiment, the velocity
of sound is given by v = 2fo(12 – 11). We found l, = 25.0 cm
and 12 = 75.0 cm. If there is no error in frequency, what will
be the maximum permissible error in the speed of sound?
(Take fo = 325 Hz)
11
489 8. The energy of an SHM is dependent on mass m, frequency
f, and amplitude A of oscillation. The relation is
a. MfIA?
b. Mfa-2
c. Mf²a-2
d. MfA
11
490 The dimensional formula for pressure
gradient is :
A ( cdot M L^{-1} T^{-2} )
B . ( M^{1} L^{-2} T^{-2} )
c. ( M^{1} L^{2} T^{-2} )
D. ( M^{1} L^{-1} T^{-3} )
11
491 Which one can be represented as the
symbol of time?
A .
в. ( F )
( c )
D. None
11
492 What is the advantage of choosing the wavelength of light as a standard of length?
A. Travels fast
B. Speed independent of location and temperature
c. No medium to travel
D. No advantage
11
493 A beam balance of unequal arm length is used by an unscruplus trader. When an object is weighed on left pan. The
weight ( i ) found to be ( W_{1} . ) When the
object is weighed on the right plan, the weight is found to be ( W_{2} ). If ( W_{1} neq W_{2} )
the correct weight of the object is
A. ( frac{W_{1}+W_{2}}{2} )
В. ( sqrt{W_{1} W_{2}} )
c. ( sqrt{W_{1}^{2}+W_{2}^{2}} )
D. ( sqrt{W_{2}^{2}-W_{1}^{2}} )
11
494 Convert ( 1 g / c m^{3} ) to ( k g / m^{3} )
A. 1000
B. 100
c. ( 0 . )
D. 10
11
495 4. The nth division of main scale coincides with (n + 1)
divisions of Vernier scale. Given one main scale division
is equal to a units. Find the least count of the vernier.
(IIT JEE, 2003)
11
496 In situation ( 2, ) if ( h_{2} ) is further decreased
then
A. cylinder will not move up an remains at its original position
B. for ( h_{2}=h / 3 ) cylinder again starts moving up
C. for ( h_{2}=h / 4 ) cylinder again starts moving up
D. for ( h_{2}=h / 5 ) cylinder again starts moving up
11
497 Which of the following conversions is
correct?
( A cdot 1 a t m=1.01 times 10^{4} mathrm{Pa} )
B. ( 1 mathrm{mm} ) of ( mathrm{Hg}=133 mathrm{Pa} )
c. 1 bar ( =10^{7} ) Pa
D. 1 torr ( =10^{2} ) Pa
11
498 The Sl unit of inductance, henry can be written as:
a) ( frac{text { weber }}{text { ampere }} )
b) ( frac{V o l t-text { second }}{text { ampere }} ) c) ( frac{text {joule}}{text {ampere}^{2}} )
d) Ohm – second
A. a & c are correct
B. a & b are correct
c. a, b & c are correct
D. all are correct
11
499 24. A body of mass m hung at one end of the spring executes
simple harmonic motion. The force constant of a spring is
k while its period of vibration is T. Prove by dimensional
method that the equation T = 2Tomlk is incorrect. Denve
the correct equation, assuming that they are related by a
power law.
11
500 73. While measuring the acceleration due to gravity by a
simple pendulum, a student makes a positive error of 1%
in the length of the pendulum and a negative error of 3%
in the value of time period. His percentage error in the
measurement of g by the relation g= 4T (UT) will be
a. 2% b. 4% c. 7% d. 10%
_____1__4ende te
b
11
501 In the context of accuracy to
measurement and significant figures in expressing results of experiment, which of the following is/are correct?
(1) Out of the measurements ( 50.14 mathrm{cm} ) and 0.00025 ampere, the first one has greater accuracy.
(2) If one travels ( 478 mathrm{km} ) by rail and 397
m. by road, the total distance traveled is
( 478 mathrm{km} )
A. Only (1) is correct
B. only (2) is correct
c. Both are correct
D. None of these is correct
11
502 Frictional force can’t be measured in
( mathbf{A} cdot mathbf{k g} ) wt
B. Newton
c. Dyne
D. ( k g m s^{-} )
11
503 The dimensional formula for impulse is:
A ( . M L T^{-2} )
в. ( M L T^{-1} )
( mathbf{c} cdot M L^{2} T^{-1} )
D. ( M^{2} L T^{-1} )
11
504 Illustration 1.26
A physical quantity x is calculated from the
a²f3
relation x=- . If the percentage error in a, b, c, and d
cud
are 2%, 1%, 3%, and 4%, respectively, what is the percentage
error in x?
11
505 n
8. The relative density of material of a body is found by
weighing it first in air and then in water. If the weight in
air is (5.00 + 0.05) Newton and weight in water is (4.00
+0.05) Newton. Then the relative density along with the
maximum permissible percentage error is
(a) 5.0 + 11%
(b) 5.0 + 1%
(c) 5.0 + 6%
(d) 1.25 + 5%
11
506 With due regard to significant figures, add the following:
a. 953 and 0.324
b. 953 and 0.625
c. 953.0 and 0.324
d. 953.0 and 0.374
A . a. ( 953 ; ) b. 954 c. 953.3 d. 953.4
B. a. ( 953 ; ) b. 955 c. 953.3 d. ( 953 . )
c. a. ( 952 ; ) b. 954 с. 953.3 d. 953.4
D. a. ( 953 ; ) b. 954 c. 953.3 d. 952.4
11
507 The dimension of ( left(frac{1}{2}right) varepsilon_{0} boldsymbol{E}^{2} ) is ( left(varepsilon_{0}right. )
permittivity of free space, Electric field)
A . ( M L T^{-} )
В. ( M L^{2} T^{-2} )
c. ( M L^{-1} T^{-2} )
D. ( M L^{2} T^{-1} )
11
508 Which of the following is incorrect
statement?
A. A dimensionally correct equation may be correct
B. A dimensionally correct equation may be incorrect
C. A dimensionally incorrect equation may be correct
D. A dimensionally incorrect equation is incorrect
11
509 Write down the number of significant figures in the following value.
( 62.00 mathrm{m} )
A. four
B. three
c. ( t w o )
D. on
11
510 32. Which of the following is the most precise instrument for
measuring length?
a. Meter rod of least count 0.1 cm
b. Vernier callipers of least count 0.01 cm
c. Screw gauge of least count 0.001 cm
d. Data is not sufficient to decide
11
511 In a experiment to measure the height of a bridge by dropping a stone into water underneath,if the error in the
measurement of times is ( 0.1 s ) at the
end of ( 2 s ),then the error in the
estimation of the height of the bridge
will be
( mathbf{A} cdot 0.49 m )
B. ( 0.98 m )
c. ( 1.96 m )
D. ( 2.12 m )
11
512 The radius of a sphere is measured to be ( (4.0+2.0) mathrm{cm} ) the maximum
percentage error in the measurement of
the volume of the sphere is
A . ( 10 % )
B. 15 %
c. ( 20 % )
D. 25 %
11
513 3. Which of the following is not equal to watt?
(a) Joule/second (b) Ampere x volt
(c) (Ampere)2 x ohm (d) Ampere/volt
11
514 The fractional change in the value of free-fall acceleration ( g ) for a particle when it is lifted from the surface to an
elevation ( boldsymbol{h}(boldsymbol{h}<<boldsymbol{R}) ) is :
A ( cdot frac{h}{R} )
в. ( frac{2 h}{R} )
( c cdot-frac{2 h}{R} )
D. ( -frac{h}{R} )
11
515 38. If C (the velocity of light) 8, (the acceleration due
to gravity), and P (the atmospheric pressure) are
the fundamental quantities in MKS system, then the
dimensions of length will be same as that of
a. Clg b. C
P C . PCg d. C-g
1
11
516 Count total number of significant figures in 0.00418
A. 5
B. 4
( c cdot 3 )
( D )
11
517 The frequency of vibration of the string is given by ( boldsymbol{v}=frac{boldsymbol{p}}{mathbf{2 l}}left[frac{boldsymbol{F}}{boldsymbol{m}}right]^{1 / 2} )
Here, p is the number of segments in the string and I is the length. The dimensional formula for m will be
( mathbf{A} cdotleft[M^{0} L T^{-1}right] )
B ( cdotleft[M L^{0} T^{-1}right] )
( mathbf{c} cdotleft[M L^{-1} T^{0}right] )
( mathbf{D} cdotleft[M^{0} L^{0} T^{0}right] )
11
518 27. What are the dimensions of gas constant?
a. [M LT-2K-41 b . [M°LT-2K-‘]
c. [M L’T-2 K-‘mol-‘1 d. [M°LT-2 K-1
11
519 The multiplication of 10.610 with 0.210 upto correct number of significant figure is
A . 2.2281
B . 2.228
( c cdot 2.23 )
D. 2.3
11
520 If velocity (V), force (F) and time (T) are chosen as fundamental quantities,
express
(i) mass and
(ii) energy in terms of ( mathrm{V}, mathrm{F} ) and ( mathrm{T} )
11
521 Round off following number upto four significant figures
( mathbf{2 . 0 0 8 2 3} )
( mathbf{A} cdot 2.008 )
в. 2.0082
c. 2.0083
D. 2
11
522 Write the number of significant digits in 0.6464:
A . 4
B. 3
( c cdot 5 )
D. None of the above
11
523 Assertion
Angle and angular displacement are dimensionless quantities.
Reason
Angle is equal to arc length divided by
radius.
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
524 What is Knot?
A. Unit of measuring wind velocity
B. Unit of measuring air pressure
C. Unit of measuring temperature
D. Condition of sky
11
525 37. The frequency fof vibrations of a mass m suspended from
a spring of spring constant k is given by f= Cm’K’, where
C is a dimensionless constant. The values of x and y are,
respectively,
11
a. 22
b.
1 1
23
1
1
c. 1 1
2-2
d. – – –
22
11
526 12. The density of a solid ball is to be determined in an
experiment in an experiment. The diameter of the ball is
measured with a screw gauge, whose pitch is 0.5 mm and
there are 50 divisions on the circular scale. The reading
on the main scale is 2.5 mm and that on the circular scale
is 20 divisions. If the measured mass of the ball has a
relative error of 2%, the relative percentage error in the
density is
a. 0.9%
b. 2.4%
c. 3.1%
d. 4.2%
(IIT JEE, 2011)
11
527 An air bubble inside water oscillates
due to some explosion with period T. If
( T propto P^{a} d^{b} E^{c} ) then determine the values
of ( a, b ) and ( c . ) Here ( P, d ) and ( E ) are the static pressure, density and total energy of explosion of water, respectively.
A ( cdot a=frac{5}{6}, b=1, c=frac{1}{3} )
B. ( a=-frac{5}{6}, b=frac{1}{2}, c=frac{1}{3} )
c. ( a=1, b=1, c=1 )
D. ( a=0, b=0, c=1 )
11
528 The S.I. unit of pole strength is
A ( . A m^{2} )
в. ( A m )
c. ( A m^{-1} )
D. ( A m^{-2} )
11
529 When a current of ( (2.50 pm 0.5) A )
flows through a wire, it develops a
potential difference of ( (20 pm 1) V . ) The
resistance of the wire is :
A. ( (8 pm 2) Omega )
в. ( (10 pm 3) Omega )
c. ( (18 pm 4) Omega )
D. ( (20 pm 6) Omega )
11
530 Which of the following is the best method to measure microscopic distances?
A. optical microscope
B. Meter scale
c. screw gauge
D. Diffraction pattern
11
531 as
nis
(JEL AU
2. The energy of a system as a function of time
E(t) = A’exp(-at), wher a=0.25-1. The measurement of
A has an errror of 1.25%. If the error in the measurement
of time is 1.50%, the percentage error in the value of E(1)
at t = 5 s
is t
(JEE Advanced, 2015)
11
532 The magnetic moment of electron is :
A. ( 9.27 times 10^{-24} ) Joule/Tesla ander
B . ( 9.27 times 10^{-24} ) Tesla/Joule
c. ( 9.27 times 10^{-23} ) Joule/Tesla
D. ( 9.27 times 10^{-23} ) Tesla/Joule
11
533 The gravitational force which acts on a body of mass ( 1 mathrm{kg} ) on the surface of the earth is
( A cdot 9.8 mathrm{N} )
B cdot ( frac{1}{9.8} ) N
c. ( 980 mathrm{N} )
D. ( frac{1}{980} mathrm{N} )
11
534 Which of the following measurements is most precise?
A. ( 4.00 mathrm{mm} )
B. 4.00 cm
c. ( 4.00 mathrm{m} )
D. ( 40.00 mathrm{m} )
11
535 The angular diameter of the sun is 1920″. If the distance of the sun from the
earth is ( 1.5 times 10^{11} mathrm{m}, ) then the linear
diameter of the sun is:
A ( cdot 2.6 times 10^{9} mathrm{m} )
В. ( 0.7 times 10^{9} mathrm{m} )
c. ( 5.2 times 10^{9} mathrm{m} )
D. ( 1.4 times 10^{9} mathrm{m} )
11
536 Using mass(M), length (L), time(T), and electric current(A) as fundamental
quantities, the dimensions of permittivity will be
( mathbf{A} cdotleft[M L T^{-1} A^{-1}right] )
в. ( left[M L T^{-2} A^{-2}right] )
( mathbf{C} cdotleft[M^{-1} L^{-3} T^{4} A^{2}right] )
D・ ( left[M^{2} L^{-2} T^{-2} Aright. )
11
537 Illustration 1.29 The distance covered by a body in time (5.0
+0.6) s is (40.0 + 0.4) m. Calculate the speed of the body.
Also determine the percentage error in the speed.
11
538 1. The main scale of a Vernier callipers reads 10 mm in
10 divisions. 10 divisions of Vernier scale coincide with
9 divisions of the main scale. When the two jaws of the
callipers touch each other, the fifth division of the Vernier
coincides with 9 main scale divisions and the zero of
the Vernier is to the right of zero of main scale. When a
cylinder is tightly placed between the two jaws, the zero
of Vernier scale lies slightly to the left of 3.2 cm and
the fourth Vernier division coincides with a main scale
division. The diameter of the cylinder is
(a) 3.09 cm
(b) 3.14 cm
(c) 3.04 cm
(d) none of these
11
539 20. The initial and final temperatures of liquid in a container
are observed to be 76.3 0.4°C and 67.7 + 0.3°C.
Determine the fall in the temperature of the liquid.
nanananc-2011 Die oberen
11
540 What is the dimensional formula of
Inductance?
( mathbf{A} cdotleft[M L^{2} T^{-2} A^{-2}right] )
B . ( left[M L^{2} T A^{-2}right] )
( mathbf{c} cdotleft[M L^{2} T^{-1} A^{-2}right. )
D ( cdotleft[M L^{2} T^{-2} A^{-1}right] )
11
541 The least count of a stop watch is ( frac{1}{5} s )
The time of 20 oscillations of a
pendulum is measured to be ( 25 s ). What is the maximum percentage error in this measurement?
( A cdot 8 % )
B. 1%
( c .0 .8 % )
D. ( 16 % )
11
542 Which of the following quantities has its unit as newton second?
A. Energy
B. Torque
c. Momentum
D. Angular momentum
11
543 While measuring the length of a wooden box, the reading at one end is ( 1.5 mathrm{cm} ) and the other end is ( 4.7 mathrm{cm} . ) What is the
length of the wooden box?
A. ( 4.7 mathrm{cm} )
B. ( 1.5 mathrm{cm} )
c. 3.2 ( mathrm{cm} )
D. 6.2 cm
11
544 Which of the following units is a unit of
power?
A. Kilowatt hour
B. Watt
c. Erg
D. Calorie
11
545 Light Year is equivalent to how much
metre?
A ( cdot 9.5 times 10^{15} )
B. ( 950 times 10^{15} )
c. ( 9.5 times 10^{19} )
D. ( 905 times 10^{15} )
11
546 sphere of radii ‘a’ and ‘b’ respectively (see figure), has volume charge density ( p=frac{A}{r}, ) Where ( A ) is a constant and ( r ) is
the distance from the centre. At the
centre of the spheres is a point charge
Q. The value of A such that the electric
field in the region between the spheres
will be constant, is:
( A )
B.
( c cdot frac{2 Q}{pi a^{2} Q} )
D. ( frac{Q}{2 pi a^{2}} )
11
547 1 JUD. DOL
14. The diameter of a cylinder is measured using a Vernier
callipers with no zero error. It is found that the zero of
the Vernier scale lies between 5.10 cm and 5.15 cm of the
main scale. The Vernier scale has 50 divisions equivalent
to 2.45 cm. The 24th division of the Vernier scale exactly
coincides with one of the main scale divisions. The
diameter of the cylinder is
a. 5.112 cm
b. 5.124 cm
c. 5.136 cm
d. 5.148 cm
(JEE Advanced, 2013)
11
548 What is the dimensional formula of
resistance?
( mathbf{A} cdotleft[M^{-1} L^{-2} T^{4} A^{-2}right] )
В ( cdotleft[M L^{2} T^{-5} A^{-3}right] )
C ( cdotleft[M^{-1} L^{-2} T^{4} A^{2}right] )
D. None of these
11
549 A cube has a side of length ( 1.2 times )
( 10^{-2} ) m. Calculate its volume?
A ( cdot 1.7 times 10^{-6} mathrm{m}^{3} )
В. ( 1.73 times 10^{-6} mathrm{m}^{3} )
c. ( 1.70 times 10^{-6} mathrm{m}^{3} )
D. ( 1.732 times 10^{-6} mathrm{m}^{3} )
11
550 ( left[M^{1} L^{2} T^{-3}right] ) are the dimensions of ( ldots )
A. pressure
B. power
c. force
D. work
11
551 c. 5.4×100
d. 4.8XI0
52. If the velocity (V), acceleration (A), and force (F) are taken
as fundamental quantities instead of mass (M), length
(L), and time (T), the dimensions of Young’s modulus
(Y) would be
a. FA2V-4
b. FA2V-5
C. FA2V-3
d. FA2V-2
001
11
552 The dimensions of ratio of magnetic
flux ( (phi) ) and permeability ( (u) ) are:
( mathbf{A} cdotleft[M^{0} L^{1} A^{1} T^{0}right. )
B . ( left[M^{0} L^{-3} T^{0} A^{1}right] )
( mathbf{c} cdotleft[M^{0} L^{-1} T^{1} A^{-1}right] )
D・ ( left[M^{0} L^{2} T^{0} A^{1}right] )
11
553 How many significant figures are there in ( 30100 ? )
( mathbf{A} cdot mathbf{1} )
B. 3
( c cdot 5 )
D. none of these
11
554 Sl unit of ( g ) i.e. the acceleration due to
gravity is
A ( cdot m^{2} / s )
B. ( m / s^{2} )
( mathrm{c} cdot s / m^{2} )
D. ( m / s )
11
555 ( 5 times 10^{7} mu s ) is equivalent to
A . ( 0.5 mathrm{s} )
B. 5 s
( c .50 mathrm{s} )
D. 500 s
11
556 6. Which of the following pairs have the same dimensions?
a. hle and magnetic flux
b. hle and electric flux
c. Electric flux and q/&g
d. Electric flux and Mol
11
557 The error in measurement caused by
positioning the eye incorrectly is called
A. parallel error
B. standard error
c. eye error
D. parallax error
11
558 The total mass of a box measured by
grocer’s balance is 2.300 kg. Two gold
pieces of masses ( 20.15 g ) and ( 20.17 g )
are added to the box. What is:(a) the
total mass of the box?(b) the difference
in the masses of the pieces to correct significant figures?
11
559 A derived dimension is something
which has some physical sense or is the combination of many fundamental
dimensions.
If true enter 1 , else enter 0
11
560 9. A student performs an experime
erforms an experiment to determine the
modulus of a wire, exactly 2 m long, by Searle’s
od. In a particular reading, the student measures the
extension in the length of the wire
on in the length of the wire to be 0.8 mm with an
ncertainty of 0.05 mm at a load of exactly 1.0 kg. The
udent also measures the diameter of the wire to be 0.4
n with an uncertainty of 0.01 mm. Take g = 9.8 ms
(exact). The Young’s modulus obtained from the reading is
a. (2.0 + 0.3) x 10″ N m-2
b. (2.0 + 0.2) x 10″ N m2
c. (2.0 + 0.1) X 10″ N m2
d. (2.0 + 0.05) x 10″ N m2 (IIT JEE, 2007)
TT
DITT
11
561 Significant figures in 0.00051 are
( A cdot 5 )
B. 3
( c cdot 2 )
D. 4
11
562 The Earth’s radius is ( 6371 k m ). The
order magnitude of the Earth’s radius is
A ( cdot 10^{3} )
B. ( 10^{2} )
( c cdot 10^{7} )
D. ( 10^{5} )
11
563 14. The period of oscillation of a simple pendulum is T =
21 L/g. The measured value of L is 20.0 cm known
to 1 mm accuracy and time for 100 oscillations of the
pendulum is found to be 90 s using a wrist watch of 1s
resolution. The accuracy in the determination of g is
(a) 2%
(b) 3%
(c) 1%
(d) 5% (JEE Main 2015)
nehmendef 10
:utine
11
564 7. The time period of oscillation of a drop depends on surface
tension o, density of the liquid p, and radius r. The relation
11
565 ( ln operatorname{arclation} F=a sin k_{1} x+b sin k_{2} T )
where ( F, x ) and ( T ) denote the force
distance and time respectively. Units of
( k_{1} ) and ( k_{2} ) are respectively a
A. meter, ( s )
B . meter ( ^{-1}, s^{-1} )
c. meter ( ^{-1}, s )
D. meter, ( s^{-1} )
11
566 In case of measurement of ( g ), if error in measurement of length of pendulum is ( 2 %, ) the percentage error in time period is1 %. The maximum error in
measurement of g is
A . 1 %
в. 2 %
c. ( 4 % )
D. no error.
11
567 The velocity of an object varies with time as ( V=A t^{2}+B t+C . ) Taking the
unit of time as ( s ) and velocity as ( m s^{-1} ) the units of ( A, B, C ) respectively are :
( mathbf{A} cdot m s^{-3}, m s^{-2}, m s^{-1} )
B . ( m s^{-2}, m s^{-1}, m s^{-3} )
c. ( m s^{-1}, m s^{-2}, m s^{-3} )
D. ( m s^{-1}, m s^{-1}, m s^{-1} )
11
568 Find the maximum possible percentage
error in the measurement of force on an
object(on mass ( mathrm{m} ) ) travelling at velocity vin a circle of radius ( r, ) if ( m=(4.0 ) plus minus 0.1 ) ( mathrm{kg}, mathrm{v}=(10 text { plus minus } 0.1) mathrm{m} / mathrm{s} ) and ( r=(8.0 text { plus minus } 0.2) m )
A. ( (50 pm 1) mathrm{N} )
B. ( 50 ±2.5 ) N
c. ( (50 pm 1.5) mathrm{N} )
D. ( (50 pm 3.5) ) N
11
569 31. In an experiment for determining the value of acceleration
due to gravity (8) using a simple pendulum, the following
observations were recorded:
Length of the string (I) = 98.0 cm
Diameter of the bob (d) = 2.56 cm
Time for 10 oscillations (T) = 20.0 s
Calculate the value of g with maximum permissible
absolute error and the percentage relative error.
11
570 The refractive index ( (mu) ) of glass is found to have the values 1.49,1.50,1.52,1.54 and 1.48
Calculate the mean value of refractive
index.
A . 1.49
в. 1.50
c. 1.51
D. 1.52
11
571 On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles,
and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy’s car got on this trip must have been
between
A ( cdot frac{290}{12.5} ) and ( frac{290}{11.5} )
В ( cdot frac{295}{12} ) and ( frac{285}{11.5} )
c. ( frac{285}{12} ) and ( frac{295}{12} )
D. ( frac{285}{12.5} ) and ( frac{295}{11.5} )
E ( cdot frac{295}{12.5} ) and ( frac{285}{11.5} )
11
572 The measured mass and volume of a
body are ( 53.63 g ) and ( 5.8 mathrm{cm}^{3} ) respectively, with possible errors of ( 0.01 g ) and ( 0.1 mathrm{cm}^{3} . ) The
maximum percentage error in density is about:
A . ( 0.2 % )
в. ( 1.74 % )
c. ( 5 % )
D. ( 10 % )
11
573 The dimensions of latent heat are –
A ( cdot M^{0} L^{2} T^{-2} )
В. ( M^{0} L^{1} T^{-2} )
c. ( M^{2} L^{0} T^{-2} )
D. ( M^{0} L^{-2} T^{-2} )
11
574 8. In an experiment, the angles are required to be measured
using an instrument. Twenty-nine divisions of the main
scale exactly coincide with the 30 divisions of the vernier
scale. If the smallest division of the main scale is half-a-
degree (0.5%), then the least count of the instrument is
(a) one minute (b) half minute
(c) one degree (d) half degree (AIEEE 2009)
iment
RAL AL
11
575 A woman weighs 500 N earth. With how much forces her body pulling up on the
earth?
A. O newton
B. Between O and 500 newton
c. 500 newton
D. between 500 and 1000 newton
E. greater than 1000 newton
11
576 Astronomical unit (AU) is the distance
between earth and the sun, 1 AU is equal
to the
A ( cdot 1.496 times 10^{8} k m )
В. ( 9.46 times 10^{12} k m )
c. ( 3.084 times 10^{13} k m )
D. ( 4.596 times 10^{15} mathrm{km} )
11
577 Density of water is
( mathbf{A} cdot 1000 k g / m^{3} )
B . ( 1 k g / m^{3} )
( mathbf{c} cdot 1000 g / mathrm{cm}^{2} )
D. ( 100 k g / m^{3} )
11
578 Complete the table choosing the right
term from the list given in brackets: ( left(10^{9}right. )
micro, ( left.mathbf{d}, mathbf{1 0}^{-mathbf{9}}, mathbf{m i} | mathbf{i}, mathbf{m}, mathbf{M}right) )
begin{tabular}{lll}
Factor & Prefix & Symbol \
( 10^{-1} ) & deci & \
( 10^{-6} ) & & ( mu ) \
& giga & G \
( 10^{6} ) & mega & \
hline
end{tabular}
11
579 The random error which exists
invariably in screw gauge is:
A. least count error
B. zero error
c. gross error
D. backlash error
11
580 Cloud chamber technique is
experimentally used for.
A. Measurement of specific charge
B. Measurement of electronic charge
C. Measurement of electronic mass
D. Studying the interaction of charges in cloud
11
581 If the energy ( (boldsymbol{E}), ) velocity ( (boldsymbol{v}) ) and force
( (F) ) be taken as fundamental
quantities, then the dimensions of
mass will be
A. ( F v^{-2} )
B. ( F v^{-1} )
( mathbf{c} cdot E v^{-2} )
D. ( E v^{2} )
11
582 If force, acceleration and time are taken
as fundamental quantities, then the dimensions of length will be
A. ( F T^{2} )
B . ( F^{-1} A^{2} T^{-1} )
c. ( F A^{2} T )
D. ( A T^{2} )
11
583 ( k g m s^{-1} ) is the Sl unit of
A. Impulse
B. Force
c. Angular velocity
D. None of these
11
584 A star is 1.45 parsec light years away. How much parallax would this star show when viewed from two locations of
the earth six months apart in its orbit
around the sun?
A .2 Parsec
B. 0.725 Parsec
c. 1.45 Parsec
D. 2.9 Parsec
11
585 How many seconds are there in a week?
A . 60480
B. 604800
c. 6048000
D. 6048
11
586 A device used to measure volume of
liquids is
This question has multiple correct options
A. Burette
B. Density bottle
c. Pipette
D. common balance
11
587 The comparison of an unknown quantity
with a known constant quantity is known as:
A. Unit
B. Scale
c. Magnitude
D. Measurement
11
588 Unit of density and relative density are
same.
A . True
B. False
11
589 55. The resistance of a metal is given by R = VII, where V is
potential difference and I is the current. In a circuit, the
potential difference across resistance is V = (8 + 0.5) V
and current in resistance, I = (4 +0.2) A. What is the value
of resistance with its percentage error?
a. (2 + 5.6%) 12
b. (2 +0.7%) 2
c. (2 + 35%) 12
d. (2 + 11.25%) 22
11
590 Let ( x ) and ( a ) stand for distance. Show that ( int frac{d x}{sqrt{a^{2}-x^{2}}}=frac{1}{a} sin ^{-1} frac{a}{x} )
dimensionally correct.
11
591 9. If x=at + bt, where x is the distance travelled by the body
in kilometres while t is the time in seconds, then the unit
of b is
(a) km/s (b) km-s (c) km/s2 (d) km-s?
11
592 (
Tau 3
7. Which of the following is not a unit of energy?
(a) W-s
(b) kg-m/sec
(c) N-m
(d) Joule
11
593 7. In C.G.S. system the magnitude of the force is 100 dynes. In
another system where the fundamental physical quantities
are kilogram, metre and minute, the magnitude of the force
(a) 0.036
(c) 3.6
(b) 0.36
(d) 36
1
.1 –
meituin mensured and ita volne in found ta
11
594 Dimensions of specific heat are :
A ( cdotleft[M L^{2} T^{-2} Kright] )
( mathbf{B} cdotleft[M L^{2} T^{-2} K^{-1}right] )
C ( cdotleft[M L^{2} T^{2} K^{-1}right] )
D・ ( left[L^{2} T^{-2} K^{-1}right] )
11
595 L10 LU-
Illustration 1.6 A calorie is a unit of heat or energy and it equals
about 4.2 J, where 1 J= 1 kg m’s. Suppose we employ a
system of units in which the unit of mass equals a kg, the unit
of length equals Bm, the unit of time is ys. Show that a calorie
has a magnitude 4.2 a’B’y in terms of the new units.
2.-2
11
596 The length, breadth and thickness of a block are given by ( l=12 mathrm{cm}, b=6 mathrm{cm} )
and ( t=2.45 mathrm{cm} . ) The volume of the
block according to the idea of significant figure should be
A ( .2 times 10^{2} )
В. ( 2 times 10^{2} c m^{3} )
c. ( 1.763 times 10^{2} c m )
D. None of these
11
597 The vertical limbs of a ( U ) shaped tube
are filled with a liquid of density ( boldsymbol{p} ) upto
a height ( h ) on each side. The horizontal
portion of the ( U ) tube having length ( 2 h ) contains a liquid of density ( 2 p . ) The ( U ) is moved horizontally with an accelerator
( boldsymbol{g} / 2 ) parallel to the horizontal arm. The
difference in heights in liquid levels in th two vertical limbs, at steady state
will be
A ( cdot frac{2 h}{7} )
B. ( frac{8 h}{7} )
( c cdot frac{4 h}{7} )
D. None of these
11
598 Determine the number of significant figure in the following.
( 3.64 times 10^{45} mathrm{kg} )
11
599 5. Choose the correct statement(s).
a. A dimensionally correct equation must be correct.
b. A dimensionally correct equation may be correct.
c. A dimensionally incorrect equation must be incorrect.
d. A dimensionally incorrect equation may be correct.
11
600 The numbers 2.745 and 2.735 on
rounding off to 3 significant figures will give:
A. 2.75 and 2.74
B. 2.74 and 2.73
c. 2.75 and 2.73
D. 2.74 and 2.74
11
601 Illustration 1.23 If there is a positive error of 50% in the
measurement of velocity of a body, find the error in the
measurement of kinetic energy.
11
602 Show that the expression of the time period ( T ) of a simple pendulum of length
( l ) given by ( T=2 pi sqrt{frac{l}{g}} ) is dimensionally
correct.
A. As in the above equation, the dimensions of both sides are same. The given formula is dimensionally correct
B. The dimension of LHS and RHS are not same
c. It cannot be solved
D. None of these
11
603 In a number without decimal, what is the significance of zeros on the right of non-zero digits? 11
604 Full name of the unit named in the
honour of a scientist is written with
A. Lower initial letter
B. Initial capital letter
c. Lower letter
D. All
11
605 If measurements for a given substance are close to the known value, but the measurements are far from each other, then you have without
Fill the appropriate
answers.
A. Accuracy, Precision
B. Precision, Accuracy
c. This situation is not possible
D. None of these
11
606 In Searle’s experiment to find Young’s
modulus, the diameter of wire is
measured as ( D=0.05 mathrm{cm}, ) the length of
wire is ( L=125 c m, ) and when a weight,
( boldsymbol{m}=20 k g ) is the put, extension in wire
was found to be ( 0.100 mathrm{cm} ). Find the
maximum permissible error in Young’s modulus ( (Y) )
11
607 Pontage II
12. a. Two plates
a. Two plates have lengths measured as (1.929.
+0.2) m. Calculate their combined length with
error limits.
The initial and final temperatures of a liquid are
measured to be 67.7 + 0.2°C and 76.3 + 0.3°C.
Calculate the rise in temperature with error limits.
TA
11
608 Aluminium has a density of ( 2.7 g / c c )
The mass of ( 15 c c ) of aluminium is
( mathbf{A} cdot 45 g )
в. ( 40.5 g )
c. ( 80 g )
D. ( 100 g )
11
609 The mass of a solid rectangle block of
iron is ( 23.6 g ) and its dimensions are
( 2.1 mathrm{cm} times 1.2 mathrm{cm} times 1.1 mathrm{cm} . ) Calculate the
density of iron.
11
610 If acceleration ( (A), operatorname{mass}(M), ) velocity
( V ) ), time ( (T) ) are the fundamental units,
then the dimensions of height will be
A ( cdot V T^{-1} M^{2} )
в. ( A M T^{-1} )
c. ( A^{-1} M^{3} V^{-1} )
D. ( A T^{2} )
11
611 Kilowatt hour (kWh) represents the unit
of
A. Power
B. Impulse
c. Momemtum
D. Energy
11
612 In an experiment the following observations were recorded
( boldsymbol{L}=mathbf{2 . 8 9 0} ) metre
( mathbf{M}=mathbf{3 . 0} mathbf{k g} )
( ell=0.87 mathrm{cm} )
( mathbf{D}=mathbf{0 . 0 4 1} mathrm{cm} )
( mathbf{g}=mathbf{9 8 1 c m} / mathbf{s e c ^ { 2 }} )
and the formula used for calculatlon of Young’s modulus ( (mathrm{Y}) ) is ( mathrm{Y}=frac{mathrm{MgL}}{pi mathrm{r}^{2} l} )
What is the maximum possible error
expressed in percentage?
A . 6.36%
B. 4.8%
c. अ%
D. 1%
11
613 Always in a physical quantity, the numerical value is inversely proportional to its units. ( N propto frac{1}{U} ) 11
614 If all measurements in an experiment
are taken up to the same number of
significant figures, then mention two possible reasons for maximum error
11
615 If accuracy of weighing machine is better than ( 1 / 2 ) percent, a student record his own mass. Choose the option that
explains the recording most accurately.
A. ( 6.43 mathrm{kg} )
B. 60 kg
( c cdot 64.3 mathrm{kg} )
D. 600kg
E. ( 643 mathrm{kg} )
11
616 13. Ampere-hour is a unit of
(a) Quantity of electricity
(b) Strength of electric current
(c) Power
(d) Energy
11
617 Two resistances ( r_{1}=(5.0 pm 0.2) Omega ) and
( r_{2}=(10.0 pm 0.1) Omega ) are connected in
parallel. Find the value of equivalent resistance with limits of percentage
error.
A ( cdot r_{p}=4 Omega pm 7 % )
B . ( r_{p}=3.3 Omega pm 14 % )
( mathbf{c} cdot r_{p}=3.3 Omega pm 3.5 % )
D . ( r_{p}=3.3 Omega pm 7 % )
11
618 Specific gravity of the body is numerically equal to of the
body.
A. apparent weight in water
B. density
c. relative density
D. thermal capacity
11
619 A piece of thread folded 6 times is placed along a ( 15 mathrm{cm} ) long measuring scale as shown in the figure. The length of the thread is between
A. ( 0.15-0.50 mathrm{m} )
B. ( 0.50 mathrm{m}-1.0 mathrm{m} )
c. ( 1.0 mathrm{m}-1.5 mathrm{m} )
D. ( 1.5 mathrm{m}-2.0 mathrm{m} )
11
620 The density of a cube is measured by measuring its mass ad length of its side. If the maximum errors in the
measurement of its mass and length are ( 3 % ) and ( 2 % ) respectively, the maximum error in the measurement of
density would be:
A . ( 12 % )
B. ( 14 % )
c. ( 7 % )
D. ( 9 % )
11
621 The moon is observed from two
diametrically opposite points on earth. The angle subtended at the moon by the
two directions of observations is ( 1^{circ} 54^{prime} )
Given the diameter of the earth to be
about ( 2.276 times 10^{7} m, ) compute the
distance of moon from the earth.
A ( cdot 1 times 10^{8} m )
В. ( 6.84 times 10^{8} mathrm{m} )
c. ( 6.84 times 10^{10} m )
D. ( 38.4 times 10^{8} mathrm{m} )
11
622 10. The best method to reduce random error is
a. To change the instrument used for measurement
b. To take help of experienced observer
c. To repeat the experiment many times and to take the
average results
d. None of the above
11
623 Which definition is correct and uses
only quantities rather than units?
A. Density is mass per cubic metre
B. Potential difference is energy per unit current
c. Pressure is force per unit area
D. speed is distance traveled per second
11
624 ( ln )
S.I. system, the value of ( varepsilon_{0} ) is:
( mathbf{A} cdot 1 C^{2} N^{-1} m^{-1} )
B ( cdot 9 times 10^{9} C^{2} N^{-1} m^{-2} )
C ( cdot frac{1}{9 times 10^{9}} C^{2} N^{-1} m^{-2} )
D. ( frac{1}{4 pi times 9 times 10^{9}} C^{2} N^{-1} m^{-2} )
11
625 What is a leap year?
A . 366
в. 365
( c .364 )
D. 363
11
626 Dimension of ( epsilon_{0} ) are
( mathbf{A} cdotleft[M^{0} L^{0} T^{0} A^{0}right] )
в. ( left[M^{0} L^{-3} T^{3} A^{3}right. )
( mathbf{c} cdotleft[M^{-1} L^{-3} T^{3} A^{1}right] )
( mathbf{D} cdotleft[M^{-1} L^{-3} T^{4} A^{2}right] )
11
627 17. In the relation y=r sin (@t – kx), the dimensions of
olk are
a. [M°C°T°)
b. [MºLT-]
c. [MºLT’)
d. [Mºltº
11
628 A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let ( boldsymbol{R} ) be the radius of its largest horizontal section. A small disturbance causes the
drop to vibrate with frequency ( v ) about
its equilibrium shape. By dimensional analysis the ratio ( frac{v}{sqrt{frac{sigma}{rho R^{3}}}} ) can be (Here
( sigma ) is surface tension, ( rho ) is density, ( g ) is
acceleration due to gravity, and ( k ) is an arbitrary dimensionless constant).
( ^{mathrm{A}} cdot frac{k rho g R^{2}}{sigma} )
в. ( frac{k rho R^{2}}{g sigma} )
c. ( frac{k rho R^{3}}{g sigma} )
D. ( frac{k rho}{g sigma} )
11
629 11 OD 10
3. Write the dimensions of the following in terms of mass,
time, length, and charge.
a. Magnetic flux
b. Rigidity modulus
(IIT JEE, 1982)
1
.
.
th
11
630 The circumference of a circle exceeds
its diameter by ( 16.8 mathrm{cm} . ) Find the radius of the circle.
11
631 The length, breadth and height of a
glass slab are respectively ( 50 mathrm{cm}, 20 mathrm{cm} )
and ( 25 c m . ) Find the order of
magnitude of volume of slab in Sl unit
A ( cdot 10^{-2} m^{3} )
В ( cdot 10^{-4} m^{3} )
( mathbf{c} cdot 10^{-3} m^{3} )
D. ( 10^{-3} mathrm{cm}^{3} )
11
632 Two clocks are being tested against a
standard clock located in a nationa
laboratory. At 12: 00: 00 noon bv the standard clock, the readings of the two
clocks are:
( begin{array}{lll} & text { Clock 1 } & text { Clock 2 } \ text { Monday } & 12: 00: 05 & 10: 15: 06 \ text { Tuesday } & 12: 01: 15 & 10: 14: 59 \ text { Wednesday } & 11: 59: 08 & 10: 15: 18 \ text { Thursday } & 12: 01: 50 & 10: 15: 07 \ text { Friday } & 11: 59: 15 & 10: 14: 53 \ text { Saturday } & 12: 01: 30 & 10: 15: 24 \ text { Sunday } & 12: 01: 19 & 10: 15: 11end{array} ) If you are doing an experiment that requires precision time interval
measurements, which of the two clocks
will you prefer?
11
633 A particle of mass ( m ) is in a uni-
directional potential field where the potential energy of a particle depends
on the ( x ) -coordinate given by ( phi_{x}= )
( phi_{0}(1-cos a x) &^{prime} phi_{0}^{prime} ) and ( ^{prime} a^{prime} ) are
constants. Find the physical
dimensions of ( ^{prime} boldsymbol{a}^{prime} & boldsymbol{phi}_{0} )
A ( cdot L^{-1}, M^{1} L^{2} T^{-2} )
B . ( L^{-2}, M^{1} L^{3} T^{-2} )
C ( cdot L^{-1}, M^{0} L^{2} T^{-1} )
D. None of these
11
634 Express the following derived units in terms of the fundamental units of
length, mass and time.
1) Speed
2) Area
3) Acceleration
4) Density
5) Volume
11
635 Find the dimensional formula of
coefficient of viscosity ( boldsymbol{eta} )
11
636 If ( bar{A} ) and ( bar{B} ) two different physical quantities, Which of the following mathematical operations is/are valid.
A. ( bar{A}+bar{B} )
в. ( overline{A . bar{B}} )
c. ( bar{A} times bar{B} )
D. Both and (b) and (c)
11
637 ILLUSTRATION 33.4
Find the thickness of the wire.
If we put a wire between jaws
Object
UU
(mm)
11
638 5. A diamond weighs 3.71 g. It is put into a box weighing
1.4 kg. Find the total weight of the box and diamond to
the correct number of significant figures.
11
.
1
1
11
639 ( 60 mathrm{cc} ) of a liquid of relative density 1.4 is mixed with ( 40 mathrm{cc} ) of another liquid of relative density 0.8. The density of the resulting mixture will be
A. ( 1.16 mathrm{g} / mathrm{cc} )
B. 2.26 g/cc
c. ( 11.6 mathrm{g} / mathrm{cc} )
D. 116 g/cc
11
640 toppr
Q Type your question
( A )
B.
( c )
( D )
11
641 The dimensional formula for Areal
velocity is :
A ( cdot M^{0} L^{-2} T^{-1} )
B . ( M^{0} L^{-2} T^{1} )
c. ( M^{0} L^{2} T^{-1} )
D. ( M^{0} L^{2} T^{1} )
11
642 Which of the following pair of quantities do not have the same dimensions?
A. Potential gradient, electric field
B. Torque, kinetic energy
c. Light year, time period
D. Impedance, reactance
11
643 In the figures given, identify the type of zero error and also suggest the correction to be made, by reasoning it
outt
11
644 The mass of a beaker is found to be
( mathbf{1 0 . 1} pm mathbf{0 . 1} ) ) gm when empty and
( (17.3 pm 0.1) g m ) when partially filled
with a liquid. What is the best value for the mass of the liquid together with the possible limits of accuracy?
A ( .(7.2 pm 0.2) g m )
в. ( (7.2 pm 0.1) g m )
( mathbf{c} .(7.1 pm 0.2) g m )
D. ( (7.2 pm 0.3) g m )
11
645 Write down the number of significant figures in ( 12.00 mathrm{N} )
A. four
B. three
c. two
D. one
11
646 COPO-0.0J)
PD-
13. You measure two quantities as A = 1.0 m + 0.2 m,
B = 2.0 m + 0.2 m. We should report correct value for
VAB as
(a) 1.4 m + 0.4 m (b) 1.41 m + 0.15 m
(c) 1.4 m + 0.3 m (d) 1.4 m 0.2 m
1
.
1
c
.
11
647 The force ( F ) is given in terms of time ( t ) and
displacement ( x ) by the equation ( F=A ) ( cos B x+C sin D t . ) The dimensional
formula of D/B is
( mathbf{A} cdotleft[M^{o} L^{o} T^{o}right] )
в. ( left[M^{circ} L^{circ} T^{-1}right] )
( mathbf{c} cdotleft[M^{o} L^{-1} T^{o}right] )
D・ ( left[M^{circ} L^{1} T^{-1}right] )
11
648 To minimise parallax error, the observer
should place the object:
( A cdot ) as near to the scale of the ruler as possible and the eye must be directly above the scale
B. as far to the scale of the ruler as possible and the eye must be directly above the scale
C. as near to the scale of the ruler as possible and the eye must be to the right of the scale
D. as near to the scale of the ruler as possible and the eye must be to the left of the scale
11
649 76. The dimensional formula for a physical quantity x is
[M-‘LT-2]. The errors in measuring the quantities M,
L, and T, respectively, are 2%,3%, and 4%. The maximum
percentage of error that occurs in measuring the quantity
x is
a.
9 b . 10
c. 14 d. 19
11
650 With the increase in temperature, the density of substance, in general,
A. increases
B. decreases
c. first increases then decreases
D. first decreases then increases
11
651 Which of the following is/are correct?
This question has multiple correct options
A. Random errors can not be estimated by repeating a measurement several (perhaps many) times.
B. Random errors can result due to unpredictable fluctuations in temperature or line voltage during experimental measurements.
C. Am impoperly “Zeroed” instrument (such as an ammeter) can result in systematic errors.
D. Large degree of precision implies accuracy.
11
652 Illustration 1.38 10 rotations of the cap of a screw gauge is
equivalent to 5 mm. The cap has 100 divisions. Find the least
count. A reading taken for the diameter of wire with the screw
gauge shows four complete rotations and 35 divisions on the
circular scale. Find the diameter of the wire.
11
653 The order of magnitude of seconds in a
day is ( 10^{x} ). What is ( x )
11
654 A diamond weighs ( 3.71 g ). It is put into a
box weighing ( 1.4 k g . ) Find the total
weight of the box and diamond to the correct number of significant figures.
11
655 9. Consider three quantities: x=
=, and z=-
CR
✓MEO
Here, 7 is the length of a wire, C is the capacitance, and
R is a resistance. All other symbols have usual meanings.
Then
a. x and y have the same dimensions.
b. x and z have the same dimensions.
c. y and z have the same dimensions.
d. None of the above three pairs have the same
dimensions.
11
656 The characteristic of a good unit is
A. It should be universally accepted
B. It should be invariable and not perishable
C. It should be easily available & easy to reproduce
D. All of these
11
657 9. A physical quantity x depends on quantities y and z as
follows: x = Ay+ B tan Cz, where A, B and C are constants.
Which of the following do not have the same dimensions?
(a) x and B
(b) Cand z-1
(c) y and BIA
(d) x and A
11
658 28. The order of magnitude of 499 is 2, then the order o
magnitude of 501 will be
a. 4
3b. 2
c. 1
d. 3
e
.
11
659 Using mass ( (M), ) length ( (L), ) time ( (T) )
and current ( (A) ) as fundamental
quantities, the dimensional formula of
permittivity is
( mathbf{A} cdotleft[M L^{-2} T^{2} Aright] )
B ( cdotleft[M^{-1} L^{-3} T^{4} A^{2}right] )
( mathbf{c} cdotleft[M L T^{-2} Aright] )
D・ ( left[M L^{2} T^{-1} A^{2}right] )
11
660 11. A length is measured as 7.60 m. This is the same as
a. 7600 mm
b. 0.0076 mm
c. 760 cm
d. 0.76 dm
11
661 If ( boldsymbol{v}=frac{boldsymbol{A}}{boldsymbol{t}}+boldsymbol{B} boldsymbol{t}^{2}+boldsymbol{C} boldsymbol{t}^{3} ) where ( mathbf{v} ) is
velocity, t is time and ( A, B ) and ( C ) are constant then the dimensional formula
of B is?
( mathbf{A} cdotleft[M^{0} L T^{0}right] )
( mathbf{B} cdotleft[M L^{0} T^{0}right] )
( mathbf{c} cdotleft[M^{0} L^{0} Tright] )
( mathbf{D} cdotleft[M^{0} L T^{-3}right] )
11
662 68. The relation tan 0 = v’lrg gives the angle of banking of
the cyclist going round the curve. Here v is the speed
of the cyclist, r is the radius of the curve, and g is the
acceleration due to gravity. Which of the following
statements about the relation is true?
a. It is both dimensionally as well as numerically
correct.
b. It is neither dimensionally correct nor numerically
correct.
c. It is dimensionally correct but not numerically.
d. It is numerically correct but not dimensionally.
11
663 The prefix used for denoting an order of
magnitude of ( 10^{6} ) is
A . Giga
B. Kilo
c. Mega
D. Micro
11
664 Find the dimensions of:
(i) Power
(ii) Forces and (iii)
Permittivity of vacuum ( left(varepsilon_{o}right) )
11
665 15. Using the expression 2d sin 0= 2, one calculates the values
of d by measuring the corresponding angles in the range
0° to 90°. The wavelength 2 is exactly known and the error
in Ois constant for all values of 0. As O increases from 0°,
a. the absolute error in d remains constant.
b. the absolute error in d increases.
c. the fractional error in d remains constant.
d. the fractional error in d decreases.
(JEE Advanced, 2013)
11
666 The number of significant figures in the numbers 672.9 and ( 2.520 times 10^{7} ) are
A .4,4
в. 3,4
c. 4,3
D. 3,3
11
667 A pendulum clock keeps correct time at
( 20^{circ} mathrm{C} . ) The correction to be made during
summer per day where the average
temperature is ( 40^{circ} C,left(alpha=10^{-5} /^{circ} Cright) )
will be:
A. 5.64 sec
B. 6.64 sec
c. 7.64 sec
D. 8.64 sec
11
668 6. Which of the following sets has different dimensions?
a. Pressure, Young’s modulus, stress
b. Emf, potential difference, electric potential
c. Heat, work done, energy
d. Dipole moment, electric flux, electric field
(IIT JEE, 2005)
11
669 Multiple Correct Answers Type Which of the following pairs have different dimensions?

This question has multiple correct options
A. Frequency and angular velocity
B. Tension and surface tension
c. Density and energy density
D. Linear momentum and angular momentum

11
670 specific resistance p of a circular wire of radius r,
resistance R, and length 1 is given by p= 1
r=0.24 +0.02 cm. R=30+ 112, and 1=4.80 +0.01 cm.
The percentage error in p is nearly
a. 7%
b. 9%
c. 13%
d. 20%
11
671 The unit of Radiation exposure is? 11
672 Light year is the
A. light emitted by the sun in one year.
B. the time taken by light to travel from sun to earth.
C. the distance travelled by light in free space in one year.
D. the time taken by earth to go once around the sun.
11
673 Four pieces of wooden sticks ( P, Q, R ) and S are placed along the length of ( 15 mathrm{cm} ) long scale as shown in figure. What is the average length of these sticks?
A . 2.0
B. 2.5 ( mathrm{cm} )
c. ( 2.6 mathrm{cm} )
D. 2.9 ( mathrm{cm} )
11
674 18. The dimensions of EoMo are
a. [LT-]
b. [LT-2]
c. [L²T-2
d. [L272
11
675 The mass ‘ ( M^{prime} ) of a stone that can be
moved by water current depends upon velocity ‘ ( V^{prime} ) of the stream, density of
water ‘ ( d ) and acceleration due to gravity
‘g’. The relation between the mass and velocity is:
( mathbf{A} cdot M propto V^{6} )
B. ( M propto V^{2} )
c. ( M propto d^{2} )
D. ( M propto V )
11
676 Which of the following functions of ( boldsymbol{A} )
and ( B ) may be performed if ( A ) and ( B ) possess different dimensions?
A ( cdot frac{A}{B} )
B. ( A+B )
c. ( A-B )
D. None
11
677 Give two examples of the fundamenta physical quantities along with their S.
units.
11
678 Point the odd one out
Hydrometer, density bottle, physical balance
A. physical balance
B. density bottle
c. hydrometer
D. NONE
11
679 Fill in the blanks with suitable units of
measurements.
The distance I walk in 10 minutes is
about one
11
680 ( alpha=frac{F v^{2}}{beta^{2}} log _{e}left(frac{2 pi beta}{v^{2}}right) ) where ( F= ) force
= velocity
Find the dimensions of ( alpha ) and ( beta )
11
681 Write down the number of significant figures in ( 0.00628 mathrm{cm} )
A. four
B. three
c. two
D. one
11
682 What is the value of 1 nano-second in
second?
A ( cdot 10^{-9} )
( 9^{-9} )
B. ( 10^{-6} )
( c cdot 10^{-8} )
D. ( 10^{-10} )
11
683 Assertion
10 decades make a century.
Reason
century makes 100 years and 1 decade
make 10 years.
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
684 Define the term standard unit. 11
685 ( 0.0008 m=8 times 10^{-x} m . ) Find ( x ) 11
686 The effect of an impulse force on the body is measured only in terms of its
A. Force
B. Moment of momentum
c. Impulse
D. None of these
11
687 2. In the formula X = 3YZ², X and Z have dimensions of
capacitance and magnetic induction, respectively. The
dimensions of Y in M.K.S. system are
(IIT JEE, 1985)
11
688 Which one of the following is not a unit of Young’s modulus?
( mathbf{A} cdot N m^{-1} )
B. ( N m^{-2} )
c. Dyne ( c m^{-2} )
D. Mega pascal
11
689 The radius of the earth is given ( 6.4 times )
( 10^{6} m . ) What is the order of magnitude of
the size of the earth?
( mathbf{A} cdot 10^{6} m )
B . ( 6 times 10^{6} mathrm{m} )
( mathbf{c} cdot 10^{7} m )
D . ( 5 times 10^{6} m )
11
690 The Sl unit of static coefficient of
friction is
A.
B. Nm
c. ( frac{N}{m} )
D. it is unit less
11
691 elation V _ N Pr4
45. In the relation V = –, where the letters have their
8 nl
usual meanings, the dimensions of V are
a. M°L T°
b. MLT-1
c. M°L-3 T-1
d. M’L T°
11
11
11
692 What will be the weight of a body of
mass ( m ) kg at the centre of the earth?
A. ( m g ) newton
B. ( m / g ) newton
c. ( m ) newton
D. 0 newton
11
693 In system called the star system we have 1 star kilogram ( =10^{20} k g .1 )
starmeter ( =10^{8} m, 1 ) starsecond ( = )
( 10^{3} )second then calculate the value of
1 joule in this system.
A ( cdot 10^{-30} ) star joule
B . ( 10^{-27} ) star joule
C ( .10^{-32} ) star joule
D. None of these
11
694 The error in the measurement of the
radius of a sphere is ( 1 % . ) Find the error in the measurement of volume?
11
695 13. An athletic coach told his team that muscle times speed
equals power. What dimensions does he view for muscle?
(a) MLT-2
(b) MLPT-2
(c) MLT
(d) L
11
696 In an experiment, the percentage of
error occurred in the measurement of
physical quantities ( A, B, C ) and ( D ) are ( 1 % ) ( 2 %, 3 % ) and ( 4 % ) respectively. Then the
maximum percentage of error in the measurement ( mathbf{X}, ) where ( boldsymbol{X}=frac{boldsymbol{A}^{mathbf{2}} boldsymbol{B}^{mathbf{1} / mathbf{2}}}{boldsymbol{C}^{mathbf{1} / mathbf{3}} boldsymbol{D}^{mathbf{3}}} )
will be
A ( cdotleft(frac{3}{13}right) % )
B. ( 16 % )
c. ( -10 % )
D. ( 10 % )
11
697 The standard quantity used for comparison is called Unit.
A. True
B. False
11
698 1 Parsec is equivalent to how much AU?
A . 206
B. 206264000
( c cdot 206264 )
D. 20600
11
699 50. If L, R, C, and V, respectively, represent inductance,
resistance, capacitance and potential difference, then the
dimensions of L/RCV are the same as those of
a. Charge
b. 1/Charge
c. Current
d. 1/Current
11
700 A gas bubble from an explosion under water oscillation with a period proportional to ( P^{a}, d^{b}, E^{c} ) where ( P ) is the
static pressure, ( d ) is the density of water
and ( boldsymbol{E} ) is the energy of explosion. Then
( a, b ) and ( c ) respectively are
A ( cdot quad-frac{5}{6}, frac{1}{2}, frac{1}{3} )
в. ( frac{1}{2}, frac{-5}{6}, frac{1}{3} )
c. ( frac{1}{3}, frac{1}{2}, frac{-5}{6} )
D. 1,1,1
11
701 Let us consider an equation ( frac{1}{2} m u^{2}= ) ( m g h, ) where ( m ) is mass of the body, ( v ) its
velocity, ( g ) is the acceleration due to
gravity and ( R ) is the Right. Check whether this equation is dimensionally
correct
11
702 The magnitude of a physical quantity consists of
A. a number and a unit
B. a number
c. a unit
D. a unit and its symbol
11
703 The speed of sound in a gas is given by ( boldsymbol{v}=sqrt{frac{gamma boldsymbol{R} boldsymbol{T}}{boldsymbol{M}}} )
( R= ) universal gas constant
( boldsymbol{T}= ) temperature
( M= ) molar mass of gas The dimensional formula of ( gamma ) is
( mathbf{A} cdotleft[M^{0} L^{0} T^{0}right. )
B . ( left[M^{0} L T^{-1}right] )
( mathbf{c} cdotleft[M L T^{-2}right] )
D cdot ( left[M^{0} L^{0} T^{-1}right] )
11
704 2. There are four Vernier scales, whose specifications are
given in Column I and the least count is given in Column
II. Match the Columns I and II with correct specification
and corresponding least count (s = value of main scale
division, n=number of marks on Vernier). Assume (n-1)
main scale divisions are equal to n Vernier divisions.
Column I
i. s = 1 mm, n= 10
ü. s=0.5 mm, n= 10
iii. s=0.5 mm, n=20
iv. S= 1 mm, n= 100
Column II
0.05 mm
0.01 mm
0.1 mm
d. 0.025 mm
11
705 A student measures the time period of
100 oscillations of a simple pendulum four times. The data set is
( 90 s, 91 s, 95 s ) and ( 92 s . ) If the minimum
division in the measuring clock is ( 1 s ) then the reported mean time should be:
A ( .92 pm 2 s )
В. ( 92 pm 5.0 s )
c. ( 92 pm 1.8 s )
D. ( 92 pm 3 ) s
11
706 Dimensional methods provide three major advantages in verification, derivation and changing the system of units. Any empirical formula that is derived based on this method has to be
verified and proportionality constants found by experimental means. The presence or absence of certain factors –
non dimensional constants or variables
cannot be identified by this method. So every dimensionally correct relation cannot be taken as perfectly correct.
The time period of oscillation of a drop
depends on surface tenson ( sigma, ) density of
the liquid ( rho, ) and radius ( r . ) The relation is
B. ( sqrt{frac{r^{2}}{rho sigma}} )
c. ( sqrt{frac{r^{3} rho}{sigma}} )
D. ( sqrt{frac{rho sigma}{r^{3}}} )
11
707 The number of significant figures in ( 6.023 times 10^{23} ) is
( mathbf{A} cdot mathbf{4} )
B. 3
( c cdot 2 )
D . 23
11
708 A block of wood weights ( 12 mathrm{kg} ) and has a relative density ( 0.6 . ) It is to be of its volume immersed. What weight of a metal is needed if the metal is on the
top of wood? [Relative density of metal =
14].
( A cdot 2 mathrm{kg} )
B. ( 4 mathrm{kg} )
( c cdot 6 mathrm{kg} )
( D cdot 8 mathrm{kg} )
11
709 The error in the measurement of radius
of a sphere is ( 2 % . ) What will be the error in the calculation of its surface area? (surface area ( left.A=4 pi r^{2}right) frac{Delta A}{A}=frac{2 Delta r}{r} )
11
710 Define density. What is the Sl units of density? 11
711 1 m is equal to
( mathbf{A} cdot 10^{-6} ) micron
B. ( 10^{6} ) micron
C ( cdot 10^{-3} ) micron
D. ( 10^{3} ) micron
11
712 Which one of the following is not the vector quantity?
A . Torque
B. Displacement
c. velocity
D. None of the above
11
713 millimeter ( _{–} ) – picometer.
A . ( 10^{9} )
B. ( 10^{-9} )
( c cdot 10^{8} )
D. ( 10^{10} )
11
714 Which of the following is not a unit of time?
This question has multiple correct options
A. Parsec
B. Light year
c. Micron
D. second
11
715 The distance travelled by light in one year is called
A . Light Year
B. Light Distance
c. Both (a) and (b)
D. None of these
11
716 Which of the following units is not a
base unit?
A. metre
B. candela
c. ampere
D. pascal
11
717 OSOVO
14. Which of the following ratios express pressure?
(a) Force/Area
(b) Energy/Volume
(c) Energy/Area (d) Force/Volume
11
718 What is the value of ( sqrt{79.62} ? )
A . 8.923
B. 8.9230
c. 8.92300
D. 8.9326
11
719 If the energy, ( E=G^{p} h^{q} c^{r}, ) where ( G ) is the
universal gravitational constant, h is the Planck’s constant and c is the
velocity of light, then the values of ( p, q ) and ( r ) are, respectively
A ( cdot-1 / 2,1 / 2 ) and ( 5 / 2 )
B. ( 1 / 2,-1 / 2 ) and ( -5 / 2 )
c. ( -1 / 2,1 / 2 ) and ( 3 / 2 )
D. ( 1 / 2,-1 / 2 ) and ( -3 / 2 )
11
720 If the value of ( 103.5 mathrm{kg} ) is rounded off to three significant figures, then the value
is
A ( cdot 103 )
B. 103.0
( c cdot 104 )
D. 10.3
11
721 Identify which of the following quantities is a scalar quantity?
A. displacement
B. mass
c. resultant
D. equilibrant
( E cdot 101 mathrm{m} / mathrm{s} ) at ( 30^{circ} ) north of east
11
722 at
b-x²
43. Write the dimensions of a x b in the relation E=
where E is the energy, x is the displacement, and t is the
time.
a. MLT b. M-‘LT’ c. MLT-2 d. MLT-2
11
723 Dimension of specific heat is:
A ( cdot M L T^{-1} K^{-1} )
B. ( M L^{2} T^{-2} K^{-1} )
c. ( M^{0} L^{2} T^{-2} K^{-1} )
D. ( M^{-1} L^{2} T^{-2} K^{-1} )
11
724 The dimensions of ( frac{1}{mu_{0} in_{0}} ) is (where
symbols have their usual menaing)
A ( cdotleft[L^{2} T^{-2}right] )
в. ( [A] )
C ( cdotleft[M L^{2} T^{-2}right] )
D. ( left[M L^{-2} T^{-2}right. )
11
725 Light years is the unit of:
A. time
B. length
c. mass
D. none of these
11
726 A uniform wire of length ( l=5 pm 0.05 mathrm{cm} )
and radius ( r=0.5 pm 0.005 mathrm{cm} ) has
mass ( boldsymbol{m}=mathbf{0 . 4}+mathbf{0 . 0 0 4 g} . ) The maximum
percentage error in its density is
( A )
B. 2
( c cdot 4 )
D. 5.8
11
727 The Sl unit of amplitude of oscillation is
A . cm
в.
( c cdot k m )
D. none of these
11
728 Assertion
Parallax method is used for measuring
distances of nearby stars only.
Reason
With increase of distance of star,
parallactic angle becomes too small to be measured accurately.
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
729 With usual notation, the following equation, said to give the distance
covered in the ( n^{t h} ) second i.e., ( S_{n}=u+ )
( a frac{(2 n-1)}{2} ) is :
A. numerically correct
B. dimensionally correct
c. both dimensionally and numerically correct
D. neither numerically nor dimensionally correct
11
730 The velocity ( v ) of a particle at timet is given by ( v=a t+frac{b}{t+c} ) where ( a, b ) and ( c ) are constants. The dimensions of ( a, b ) and ( c ) are respectively:
( mathbf{A} cdot L T^{-2}, L ) and ( T )
B. ( L^{2}, T ) and ( L T^{2} )
c. ( L T^{2}, L T ) and ( L )
D. ( L, L T ) and ( T^{2} )
11
731 The measures of length and breadth of a rectangle are ( (30 pm 3 %) ) and ( (10 pm 0.5 %) ) metre. Calculate the percentage error in
the perimeter.
A . 2.4%
в. 3.5%
c. ( 1.9 % )
D. 4%
11
732 One horse power is equal to
A . ( 1000 mathrm{W} )
B. ( 500 W )
c. ( 764 W )
D. ( 746 W )
11
733 The relative density of substance is numerically equal to its density in the system of units. 11
734 Which pair of following quantities has dimensions different from each other.
A. Impulse and linear momentummmmmmmmm
c. Moment of inertia and moment to force
D. Young’s modulus and pressure
11
735 Sl unit of ( G ) is ( N m^{2} k g^{-2} . ) Which of the following can also be used as the Sl unit
of G?
A ( cdot m^{3} k g^{-1} s^{-2} )
B . ( m^{2} k g^{-2} s^{-1} )
c. ( m k g^{-3} s^{-1} )
D. ( m^{2} k g^{-3} s^{-2} )
11
736 In the relation ( boldsymbol{F}=boldsymbol{a} sin boldsymbol{k}_{1} boldsymbol{x}+ )
( boldsymbol{b} sin boldsymbol{k}_{2} boldsymbol{t}, ) the units ( (mathrm{Sl}) ) of ( frac{boldsymbol{k}_{1}}{boldsymbol{k}_{2}} ) is
( (F, x & t ) have usual meanings)
( mathbf{A} cdot s / m )
B. sm
( c cdot s t )
D. s/t
11
737 12. A spectrometer gives the following reading when used to
measure the angle of a prism.
Main scale reading: 58.5 degree
Vernier scale reading: 09 divisions
Given that 1 division on main scale corresponds to
0.5 degree. Total divisions on the vernier scale is 30 and
match with 29 divisions of the main scale. The angle of
the prism from the above data:
(a) 58.59 degree (b) 58.77 degree
(c) 58.65 degree (d) 59 degree (AIEEE 2012)
11
738 11. In an experiment, the following observation’s were
recorded : L=2.820 m, M=3.00 kg, 1=0.087 cm, Diameter
D = 0.041 cm Taking g = 9.81 m/s2 using the formula,
Y=
v_4MgL
* , the maximum permissible error in Y is
(a) 7.96%
(c) 6.50%
(b) 4.56%
(d) 8.42%
11
739 square centimetres = 1
square decimetre ( left(d m^{2}right) )
A . 100
B . 10
c. 1000
D. ( 0 . )
11
740 ( N m^{-1} ) is the Sl unit of:
A. viscosity
B. spring constant
c. surface tension
D. both B and C
11
741 A wire has a mass ( (0.3 pm 0.003) g ) radius ( (0.5 pm 0.005) mathrm{mm} ) and length (6 土 ( 0.06) mathrm{cm} . ) The maximum percentage error in the measurement of its density is –
( A )
B. 2
( c cdot 3 )
D. 4
11
742 The gravitational unit of force in the metric system is
A . gwt
B.
c. ( mathrm{kg} ) wt
D. None of these
11
743 1. The period of oscillation of a simple pendulum is given
by T = 21, where l is about 100 cm and is known to
Vg
have 1 mm accuracy. The period is about 2 s. The time of
100 oscillations is measured by a stop watch of least count
0.1 s. The percentage error in g is
(a) 0.1% (b) 1% (c) 0.2% (d) 0.8%
11
744 If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as fundamental units, the dimensions
of gravitational constant (G) are:
A ( cdot c^{0} g p^{-3} )
B ( cdot c^{2} g^{3} p^{-2} )
C. ( c^{0} g^{2} p^{-1} )
D cdot ( c^{2} g^{2} p^{-2} )
11
745 The dimensional formula for plank’s
constant and angular momentum are
( mathbf{A} cdotleft[M L^{2} T^{-2}right] ) and ( left[M L T^{-1}right] )
B ( cdotleft[M L^{2} T^{-1}right] ) and ( left[M L^{2} T^{-1}right] )
( mathbf{c} cdotleft[M L^{3} T^{1}right] ) and ( left[M L^{2} T^{-2}right] )
D・ ( left[M L^{2} T^{-1}right] ) and ( left[M L^{2} T^{-2}right] )
11
746 A student uses a simple pendulum of
exactly 1 m length to determine ( g ), the
acceleration due to gravity. He uses a
stopwatch with the least count of 1 sec
for this and records 40 seconds for 20
oscillations. For this observation, which
of the following statements is(are)
true?
This question has multiple correct options
A. Error ( Delta T ) in measuring ( T ), the time period, is 0.05 seconds.
B. Error ( Delta T ) in measuring ( T ), the time period, is 1 second.
C. Percentage error in the determination of ( g ) is ( 5 % )
D. Percentage error in the determination of ( g ) is ( 2.5 % )
11
747 The dimensional formula for Magnetic
induction is :
( mathbf{A} cdot M T^{-1} A^{-1} )
B. ( M T^{-2} A^{-1} )
( mathrm{c} cdot M L A^{-1} )
D. ( M T^{-2} A )
11
748 11. The number of significant figures can reduce in
a. Addition
b. Subtraction
c. Multiplication
d. Division
11
749 Find density when a mass of ( 9.23 mathrm{kg} ) occupies a volume of ( 1.1 m^{3} ) with due
regard to significant figures.
( mathbf{A} cdot 8.4 k g / m^{3} )
B. ( 8.39 k g / m^{3} )
( mathbf{c} cdot 8.3 k g / m^{3} )
D. None of the above
11
750 Light year is a measurement of
A. Speed of aeroplanes
B. Speed of light
c. Stellar distances
D. speed of rockets
11
751 The mass of the electron is given ( 9.1 times ) ( 10^{-31} k g . ) Find the order of magnitude of
the number of electrons of ( 1 k g )
( mathbf{A} cdot 10^{31} )
B. ( 10^{-30} )
( c cdot 10^{3} )
D. ( 10^{-31} )
11
752 The length, breadth and thickness of a block are measured with the help of a
meter scale. given ( ell=(5.12+0.01) mathrm{cm}, mathrm{b} )
( =(10.15+0.01) mathrm{cm}, mathrm{t}=(5.28+0.01) mathrm{cm} . ) The
percentage error in volume is:
A . 0.64%
B. 0.28%
c. 0.37%
D. 0.48%
11
753 In classical physics the force ( F ) acting on a body is assumed to be the product of mass ( mathrm{m} ) and acceleration a.lf ( mathrm{m}=2.31 )
( mathrm{kg} ) and acceleration is ( 3.123 mathrm{m} / mathrm{s}^{2} ), then taking into account significant figures the force ( F ) should be reported as
A. ( 7.21413 mathrm{N} )
B. 7.2141
c. 7.214 N
D. 7.21 N
11
754 The Sl unit of gravitational potential is :
A. Joule/kg
B. Joule^ /kg
c. kg/Joule
D. Joule/kg ( ^{2} )
11
755 Which one of the following has the same
dimension as that of time, if ( boldsymbol{R} ) is
resistance, ( L ) inductance and ( C ) is
capacitance?
A ( . R C )
B . ( sqrt{L C} )
c. ( frac{L}{R} )
D. All of the above
11
756 Which of the quantity consists of unit
as m/sec?
A. Speedd
B. Distance
c. weight
D. Time period
11
757 If L and R denote inductance and
resistance, respectively, then the dimensions of L/R are
A ( cdot M^{1} L^{0} T^{0} Q^{-1} )
В. ( M^{0} L^{0} T Q^{0} )
c. ( M^{0} L^{1} T^{-1} Q^{0} )
D. ( M^{-1} L T^{0} Q^{-1} )
11
758 In the density measurement of a cube, the mass an edge length are measured
as ( (mathbf{1 0 . 0 0} pm mathbf{0 . 1 0}) k g ) and
( (0.10 pm 0.01) m, ) respectively. The error
in the measurement of density:
( mathbf{A} cdot 0.10 k g / m^{3} )
в. ( 0.31 k g / m^{3} )
( mathbf{c} cdot 0.07 k g / m^{3} )
D. ( 0.01 k g / m^{3} )
E. No answer
11
759 When equal volumes of two liquids are mixed,the specific gravity of mixture is
( frac{7}{2} . ) When equal masses of the same two liquids are mixed, the specific gravity is ( frac{12}{7} . ) The specific gravities of two liquids
are:
A. 1 and 6
B. 2 and 6
( c cdot 2 ) and 4
D. 3 and 6
11
760 Wut 15 u pullage II move
16. The radius of a sphere is measured to be (2.1 +0.5) cm.
Calculate its surface area with error limits.
11
761 If the unit of tension is divided by the unit of surface tension the derived unit
will be same as that of
A . mass
B. length
c. area
D. work
11
762 What
9. Erg-m-‘ can be the unit of measure for
(a) Force
(b) Momentum
(c) Power
(d) Acceleration
.
1 anota
11
763 Sl unit of G in Newton’s law of
Gravitation is :
A ( cdot N^{2} m^{2} / k g )
в. ( N m^{2} / k g )
c. ( N m / k g )
D. ( N m^{2} / k g^{2} )
11
764 The diameter of a wire as measured by
screw gauge was found to be
2.620,2.625,2.628 and ( 2.626 mathrm{cm} )
Calculate absolute error in each
measurement.
A ( . Delta a_{5}=2.626-2.626=+0.000 mathrm{cm} )
в. ( Delta a_{4}=2.626-2.626=0.000 mathrm{cm} )
C. ( Delta a_{3}=2.626-2.630=-0.004 mathrm{cm} )
D. All of these
11
765 Burette and Pipette are used to
measure mass.
A . True
B. False
11
766 The refractive index ( (mu) ) of glass is found to have the values
1.49,1.50,1.52,1.54 and 1.48
Calculate the mean value of refractive
index.
11
767 State whether given statement is True or False.

A quantity which can be represented completely by magnitude only, is called a vector quantity.
A. True
B. False

11
768 The apparent weight of a body, weighing
M kg, during free fall is:
A. less than M kg wt
B. more than M kg wt
c. equal to M kg wt
D. zero
11
769 The radius of the sphere is ( 1.41 mathrm{cm} . ) The volume of sphere to an appropriate number of significant figures will be:
A ( cdot 11.7 c m^{3} )
B. ( 11.74 mathrm{cm}^{3} )
( mathbf{c} cdot 12 c m^{3} )
D. ( 11.736 mathrm{cm}^{3} )
11
770 nanometer is ( _{-1-} ) centimeter
A ( cdot 10^{-8} )
B. ( 10^{-7} )
( mathrm{c} cdot 10^{-9} )
D. ( 10^{-6} )
11
771 Illustration 1.35 To find the value of g using simple
pendulum, T = 2.00 s and 1=1.00 m were measured. Estimate
maximum permissible error in g. Also find the value of a
11
772 In the given figure, find the magnitude
and nature of zero error
11
773 Three measurement are made as
( 18.425 mathrm{cm} 7.21 mathrm{cm} ) and ( 5.0 mathrm{cm} . ) The
addition should be written as then:
A. ( 30.635 mathrm{cm} )
B . ( 30.64 c m )
c. ( 30.63 c m )
D. ( 30.6 mathrm{cm} )
11
774 67. A student writes four different expressions for the
displacement y in a periodic motion as a function of time
t, a as amplitude, T as time period. Which of the following
can be correct?
2nt
a. y = aT sin
T
b.
y = a sin Vt
11
775 How watt is related to the fundamental
units?
A ( cdot mathrm{kg} mathrm{m}^{2} s^{-3} )
B. ( mathrm{kg} mathrm{m}^{2} s^{-2} )
( mathrm{c} cdot mathrm{Nm} s^{-1} )
D. Nm
11
776 In a new set of units, unit of mass is 10
kg, unit of length is ( 1 mathrm{km} ) and unit of time is 1 minute. The value of 1 joule in this new hypothetical system is
A ( cdot 3.6 times 10^{-4} ) new units
B. ( 6 times 10^{7} ) new units
c. ( 10^{11} ) new units
D. ( 1.67 times 104 ) new units
11
777 49. If E, M, J, and G, respectively, denote energy, mass,
angular momentum, and gravitational constant, then
EJMG has the dimensions of
a. Time b. Angle c. Mass d. Length
50 If I R andy respectively represent inductance
11
778 An atmosphere
A. is a unit of pressure
B. is a unit of force
C . gives us an idea of composition of air
D. is the height above which there is no air
11
779 If ( 1 mathrm{g} mathrm{cm}^{-3}=10^{3} mathrm{kg} mathrm{m}^{-3} ) then
( 10^{6} k g m^{-3}= )
A ( cdot 10^{-3} g c m^{-3} )
В ( cdot 10^{6} g c m^{-3} )
( mathbf{c} cdot 10^{3} g c m^{-3} )
D. ( 10^{-6} g c m^{-3} )
11
780 A force is given by ( boldsymbol{F}=boldsymbol{a} boldsymbol{t}+boldsymbol{b} boldsymbol{t}^{2}, ) where ( boldsymbol{t} )
is time, the dimensions of ( a ) and ( b ) are
respectively:
( mathbf{A} cdotleft[M L T^{-4}right] ) and ( left[M L T^{-1}right] )
B – ( left[M L T^{-1}right] ) and ( left[M L T^{0}right] )
( mathbf{c} cdotleft[M L T^{-3}right] ) and ( left[M L T^{-4}right] )
D cdot ( left[M L T^{-3}right] ) and ( left[M L T^{0}right] )
11
781 Sl unit of electric polarisation is
A ( cdot C m^{-2} )
B. coulomb
c. ampere
D. volt
11
782 If the units of length and force are increased four times, then unit of energy will
A. becomes 8 times
B. becomes 16 times
c. decrease 16 times
D. increase 4 times
11
783 21. A capacitor of capacitance C = 2.0+ 0.1 uF is charged to
a voltage V = 20 + 0.2 V. What will be the charge on
the capacitor? Use Q = CV.
11
784 The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of
the plate. If the maximum errors in the
measurement of force and length are respectively ( 4 % ) and ( 2 % ), then the maximum error in the measurement of
pressure is?
A . ( 1 % )
B. 2%
( c .6 % )
D. ( 8 % )
11
785 The CGS unit of pressure is
A . dyne ( c m^{-2} )
B. ( N m^{-2} )
c. ( J m^{-2} )
D. dyne ( c m^{-3} )
11
786 Archaeologists often come to different
conclusions when studying the earliest
fossils due to
A. The fact that a few countries limit access to the
artifacts
B. The fact that the universal process for dating the remains is problematic
C. The fact that many fossils are decaying
D. The limited amount of archaeological remains
E. Fear of upsetting religious communities
11
787 53. The percentage errors in the measurement of mass and
speed are 2% and 3%, respectively. How much will be
the maximum error in the estimation of KE obtained by
measuring mass and speed?
a. 5% b. 1% c. 8% d. 11%
11
788 9. The quantities A and B are related by the relation, m =
A/B, where m is the linear density and A is the force. The
dimensions of B are of
(a) Pressure
(b) Work
(c) Latent heat
(d) None of the above
11
789 Using Dimensional analysis convert
newton into dyne.
11
790 A thermometer reads ( 0^{circ} mathrm{C} ) as ( 10^{circ} mathrm{C} ) and
( 100^{circ} mathrm{C} ) as ( 90^{circ} mathrm{C} ) then
Find the correct temperature if the
thermometer reads ( 20^{circ} mathrm{C} )
A ( cdot 20^{circ} mathrm{C} )
B . ( 12.5^{circ} mathrm{C} )
( mathrm{c} cdot 25^{circ} mathrm{C} )
D. ( 30^{circ} mathrm{C} )
11
791 The respective number of significant figures for the numbers 6.320,6.032 0.0006032 are then
A .3,4,8
B. 4,4,8
( c cdot 4,4,4 )
D. 4,3,4
11
792 5. In the above problem, the dimensional formula for RT is
same as that of
a. Energy
b. Force
c. Specific heat
d. Latent heat
11
793 What is the Sl unit of electric charge?
A . coulombs
B. amperes
c. volts
D. watts
11
794 4. The number of significant figures in 0.06900 is
(a) 5 (6) 4 (c) 2 (d) 3
11
795 With due regard to significant figures, the value of ( 46.7-10.04 ) is :
A. 36.7
B. 36.00
c. 36.66
D. 30.6
11
796 In an experiment, the values of two
resistances were measured as ( boldsymbol{R}_{1}= )
( (5.00 pm .2) Omega ) and ( R_{2}=(10.00 pm .1) Omega )
The percentage error in the combined resistance in parallel is :
A ( .(4.46 %) )
B. ( (7.00 %) )
( c .(5.55 %) )
D. ( (3.35 %) )
11
797 What is the largest distance (in a straight line) that can be measured
with a meter scale of length ( 1 mathrm{m} ) and smallest division of ( 1 mathrm{mm} ) ?
( mathbf{A} cdot 1 mathrm{mm} )
в. ( 1 mathrm{m} )
c. ( 100 mathrm{m} )
D. No upper limit exists for measurement of length with meter scale.
11
798 If the unit of length is doubled and that of mass and time is halved, the unit of
energy will be :
A. doubled
B. 4 times
( c .8 ) times
D. same
11
799 Which of the following does not has fundamental unit?
A. Mass
B. Time
c. Force
D. Electric current
11
800 The total height of 10 identical coins each of thickness ( 0.5 mathrm{cm} ) placed one over the other will be ( 50 mathrm{mm} )
A. True
B. False
11
801 If universal gravitational constant ( (G) ) speed of light ( (c), ) and time (t) are base units then the dimensional formula of
mass can be represented as?
A ( cdotleft[G^{1} c^{3} t^{1}right] )
( mathbf{B} cdotleft[G^{-1} c^{3} t^{1}right] )
C. ( left[G^{-1} c^{-2} t^{-1}right] )
( mathbf{D} cdotleft[G^{1} c^{-3} t^{-1}right] )
11
802 Pressure depends on distance as, ( mathbf{p}= ) ( frac{boldsymbol{alpha}}{boldsymbol{beta}} exp left(-frac{boldsymbol{alpha} mathbf{z}}{mathbf{k} boldsymbol{theta}}right), ) where ( boldsymbol{alpha}, boldsymbol{beta} ) are constants
( mathbf{z} ) is distance, ( mathbf{k} ) is Boltzman’s constant
and ( theta ) is temperature. The dimension of
( beta ) are
( mathbf{A} cdot mathbf{M}^{o} mathrm{L}^{o} mathrm{T}^{o} )
B. ( mathrm{M}^{-1} mathrm{L}^{-1} mathrm{T}^{-1} )
c. ( mathrm{M}^{circ} mathrm{L}^{2} mathrm{T}^{circ} )
D. ( mathrm{M}^{-1} mathrm{L}^{1} mathrm{T}^{2} )
11
803 The standard quantity, used for comparison, is called fundamental
quantity.
A. True
B. False
11
804 Which is the smallest unit of time?
A. Second
B. Minute
c. Hour
D. Year
11
805 In an experiment, the refractive index of glass was observed to be
1.45,1.56,1.54,1.44,1.54 and 1.53
Calculate relative error.
11
806 2. If u, and uy are the units selected in two systems of
measurement and n, and n2 their numerical values, then
(a) nju, = n2u2
(b) nju, + n2u2 = 0
(c) nin2 = uju2
(d) (n +u) = (n2 + uz)
11
807 There should be a full stop at the end of a symbol for units.
A. True
B. False
11
808 f ( boldsymbol{n}(boldsymbol{A})=mathbf{4}, boldsymbol{n}(boldsymbol{B})=boldsymbol{3}, boldsymbol{n}(boldsymbol{A} times boldsymbol{B} times )
( C)=24, ) then ( n(C)=? )
( A cdot 2 )
B.
( c cdot 12 )
D. None of these
11
809 State whether the following statement
is True or False.
The prefix used for ( 10^{3} ) is kilo.
A. True
B. False
11
810 The density of ( O_{2} ) at ( mathrm{NTP} ) is ( 1.429 mathrm{g} / mathrm{L} ) the standard molar volume:
( mathbf{A} cdot 22.4 L )
B. ( 11.2 L )
c. ( 33.6 L )
D. ( 5.6 L )
11
811 The mass of a box measured by a grocer’s balance is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. The total mass of the
box is:
A. 2.3 kg
B. 2.34 kg
c. ( 2.340 mathrm{kg} )
D. 2.3403 kg
11
812 Illustration 1.39 The following observations were taken for
determining the surface tension of water by capillary tube
method: diameter of capillary, D = 1.25 x 10 m and rise of
water in capillary, h = 1.45 x 10-2 m. Taking g = 9.80 ms?
and using the relation T = (rgh/2) x 10′ Nm’, what is the
possible error in measurement of surface tension T?
a. 2.4% b. 15% c. 1.6% d. 0.15%
11
813 47. The relative density of a material of a body is found by
weighing it first in air and then in water. If the weight
of the body in air is W = 8.00+ 0.05 N and the weight
in water is W = 6.00 0.05 N, then the relative density
Pr = W/(W -W) with the maximum permissible error
is
a. 4.00+ 0.62%
b. 4.00+ 0.82%
c. 4.00 +3.2% 1 d. 4.00 +5.62%
11
814 One micron is equal to
( mathbf{A} cdot 10^{6} m )
В ( cdot 10^{3} m )
( mathbf{c} cdot 10^{-6} m )
D. ( 10^{-3} m )
11
815 The dimensions of ( epsilon_{0} ) (permittivity in
free space) is
( mathbf{A} cdot M L^{2} T^{4} A^{2} )
B. ( M L^{-3} T^{2} A^{2} )
( mathbf{c} cdot M^{-1} L^{3} T^{4} A^{2} )
D. ( M L^{3} T^{2} A^{2} )
E ( cdot M^{-1} L^{-3} T^{4} A^{2} )
11
816 The accuracy in the measurement of
speed of light measured as ( 3.00 times ) ( 10^{8} m / s ) is :
A. ( 30 % )
B. ( frac{1}{3} % )
c. ( 3 % )
D. ( frac{1}{30} % )
11
817 The distance of a galaxy is ( 56 times 10^{25} m )
Assume the speed of light to be ( 3 x )
( 10^{8} m s^{-1} . ) Express order of magnitude of
time taken by light travelled to the galaxy.
11
818 The symbol for units should be written with a small letter
A . True
B. False
11
819 The time ( t, ) of a complete oscillation of a simple pendulum of length ( l ) is given by ( t=2 pi sqrt{frac{l}{g}} ) where ( g ) is gravitational constant. Find the approximate percentage of errors in ( t ) when the
percentage of error ( l ) is ( 1 % )
11
820 A physical parameter a can be determined by measuring the parameters b, ( c, d ) and e using the relation ( a=b^{alpha} c^{beta} d^{gamma} e^{delta} . ) If the maximum
errors in the measurement of ( b, c, d ) and
e are ( b_{1} %, c_{1} %, d_{1} % ) and ( e_{1} %, ) then find
the maximum error in the value of a
determined by the experiment.
11
821 The resistance ( boldsymbol{R}=frac{boldsymbol{V}}{boldsymbol{I}} ) where ( boldsymbol{V}= )
( (100 pm 5) V ) and ( I=(10 pm 0.2) A . ) The
percentage error in ( mathrm{R} ) is?
A ( .5 .2 % )
в. ( 4.8 % )
c. ( 7 % )
D. ( 3 % )
11
822 Two solids ( A ) and ( B ) float in water. It is
observed that ( A ) floats with half of its
volume immersed and B floats with ( 2 / 3 ) of its volume immersed. The ratio of
their densities is
A .4: 3
B. 3:4
( c cdot 2: 3 )
D. 3:2
11
823 Units of plane angle is 11
824 36. Of the following quantities, which one has the dimensions
different from the remaining three?
a. Energy density
b. Force per unit area
c. Product of charge per unit volume and voltage
d. Angular momentum per unit mass
11
825 4. The mean time period of second’s pendulum is 2.00 s and
mean absolute error in the time period is 0.05 s. To express
maximum estimate of error, the time period should be
written as
(a) (2.00 0.01) (b) (2.00 +0.025) s
(c) (2.00 +0.05) (d) (2.00 + 0.10) s
11
826 22. The resistance R= VII, where V= (100 + 5) V and I = (10
+0.2) A. Find the percentage error in R.
11
827 If error in measurement of radius of a
sphere is ( 1 %, ) what will be the error in
measurement volume?
A . ( 1 % )
B. ( frac{1}{3} % )
( c .3 % )
D. None of these
11
828 The distance between two places is 25
km. Write the magnitude of the measurement.
( A cdot k m )
B. distance
( c cdot 25 )
D. two
11
829 What is the need for measurement of a
physics quantity?
11
830 What is the dimensional formula of
dynamic viscosity?
( mathbf{A} cdotleft[m^{1} L^{-1} T^{-2}right] )
B. ( left[m^{1} L^{1} T^{-1}right] )
C. ( left[m^{1} L^{-1} T^{-1}right] )
( mathbf{D} cdotleft[m^{1} L^{1} T^{1}right] )
11
831 Illustration 1.9 Check the accuracy of relation v2 – u? =
2as, where y and u are final and initial velocities, a is the
acceleration, and s is the distance.
2 2
11
832 The length and breadth of a rectangular sheet are ( 16.2 mathrm{cm} ) and ( 10.1 mathrm{cm} ) respectively. The area of the sheet in
appropriate significant figures and error is:
( mathbf{A} cdot 164 pm 3 c m^{2} )
В. ( 163.62 pm 2.6 mathrm{cm}^{2} )
c. ( 163.6 pm 2.6 mathrm{cm}^{2} )
D. ( 163.62 pm 3 c m^{2} )
11
833 LOUIUIU
O
12. If the unit of length and force be increased four times, then
the unit of energy is
(a) Increased 4 times (b) Increased 8 times
(c) Increased 16 times (d) Decreased 16 times
11
834 ILLUSTRATION 33.2 Find the thickness of the object using the
defected vernier calipers.
0 mm
10
20
A
30
40
501
0.1 mm
Om 10 20 30 40 501
Auuuuuuuuuuuuuu
0.1 mm
11
835 A body moves with a velocity of ( 36 mathrm{km} )
( boldsymbol{h}^{-1} . ) What is the value of the velocity in
( m s^{-1} ? )
11
836 8. In terms of potential difference V, electric current I,
permittivity Eo, permeability Mo and speed of light c, the
dimensionally correct equations(s) is (are)
a. Mol2 = εV2
b. Mol = MOV
c. 1 = EV
d. Mocl = €, V
(JEE Advanced, 2015)
11
837 4. A force F is given by F = at + bt, where t is time. What
are the dimensions of a and b?
(a) MLT-3 and MLT4 (b) MLT-3 and MLT-4
(c) MLT-1 and MLTº (d) MLT 4 and MLT!
11
838 Exa is used as prefix in SI system. True =
( 1, ) false ( =0 )
11
839 The mean length of an object is ( 5 mathrm{cm} ) Which of the following measurements is most accurate?
A ( .4 .9 mathrm{cm} )
B . ( 4.805 mathrm{cm} )
( c .5 .25 m )
D. ( 5.4 mathrm{cm} )
11
840 I flowing per second per unit area
58. The mass of the liquid flowing per second per
of cross section of the tube is proportional to
where P is the pressure difference and v is the velocity,
then the relation between x and y is
a. x=y
b. x=-y
c. y² =x long do y=-x²
12.
11
841 The heat generated in a circuit is given
by ( Q=I^{2} R t, ) where I is current, ( mathrm{R} ) is
resistance and t is time. If the
percentage errors in measuring I, R and ( t ) are ( 2 %, 1 % ) and1 ( %, ) respectively, then the maximum error in measuring heat will be
A . ( 2 % )
B. ( 3 % )
c. ( 4 % )
D. ( 6 % )
11
842 15. The mean length of an object is 5 cm. Which of the
following measurements is most accurate?
(a) 4.9 cm
(b) 4.805 cm
(c) 5.25 cm
(d) 5.4 cm
11
843 Mankind has existed for about ( 10^{6} )
years whereas the universe is about
( 10^{10} ) years old. If the age of universe is taken to be one day, for how many seconds has the mankind existed?
A . ( 10 mathrm{sec} )
B. 8 sec
c. 8.64 sec
D. 64 sec
11
844 Total mechanical energy ( boldsymbol{E} ) of an object
of mass ( m ), at a height ( h ) above the
ground is given by the relation ( boldsymbol{E}=boldsymbol{m} boldsymbol{g} boldsymbol{h}+frac{boldsymbol{p}^{2}}{2 boldsymbol{m}} )
Find the dimension of ( mathrm{p} .(g= ) acceleration due to gravity)
11
845 ( 1 mathrm{kg} mathrm{fcm}^{-2} )
( mathrm{Nm}^{-2} )
A ( cdot 10^{3} )
B . ( 10^{5} )
( c cdot 10^{4} )
( D cdot 10^{6} )
11
846 The Sl unit for mass is kg.
A. True
B. False
11
847 Curie is the unit of
A. decay constant
B. radio-activity
c. half-life
D. average life
11
848 The error in the measurement of length
of a simple pendulum is ( 0.1 % ) and error in the time period is ( 2 % ). The possible maximum error in the quantity having dimensional formula ( L T^{-2} ) is
A . ( 1.1 % )
в. ( 2.2 % )
c. ( 4.1 % )
D. 6.1%
11
849 How is the following derived unit related to the fundamental units?
1) joule
A . ( N m s^{-1} )
в. ( N m )
c. ( k g m^{2} s^{-1} )
D. ( k g m^{2} s^{-2} )
11
850 The specific resistance ( rho ) of a circular wire of radius ( r, ) resistance ( R, ) and length
is given by ( rho=pi r^{2} R / l . ) Given: ( r= )
( mathbf{0 . 2 4} pm mathbf{0 . 0 2 c m}, boldsymbol{R}=mathbf{3 0} pm mathbf{1 Omega}, ) and ( boldsymbol{l}= )
( 4.80 pm 0.01 c m . ) The percentage error in
( rho ) is nearly:
A . ( 7 % )
в. ( 9 % )
c. ( 13 % )
D. 20%
11
851 13. In a system of units if force (F), acceleration (A) and time
(T) are taken as fundamental units, then the dimensional
formula of energy is
(a) FAPT (b) FAT? (c) FAT (d) FAT
11
852 1. If R is resistance, L is inductance, C is capacitance, H is
latent heat, and s is specific heat, then match the quantity
given in Column I with the dimensions given in Column
Column I
Column II
LC
a. L27-2
LR
b. Ľ21-
21
ci je
M²LAT-SAA
11
853 A physical quantity x depends on
quantities ( y ) and ( z ) as follows ( : x= )
( boldsymbol{A} boldsymbol{y}+boldsymbol{B} boldsymbol{t a n}left(boldsymbol{C}_{z}right), ) where ( boldsymbol{A}, mathbf{B} ) and ( boldsymbol{C} ) are
constants. Which of the followings do not have the same dimensions?
A. ( x ) and ( B )
B. ( c ) and ( z^{-} )
c. y and B/A
D. x and A
11
854 Write down the number of significant figures in the following value. ( mathbf{1 2 0 0} boldsymbol{N} )
A .4
B. 3
( c cdot 2 )
D.
11
855 When 13546 is rounded off to four
significant figures, it becomes:
This question has multiple correct options
A . 1355
B. 13550
C. ( 1355 times 10^{1} )
D. 135.5
11
856 Pressure ( boldsymbol{P}_{boldsymbol{r}}=frac{boldsymbol{3} boldsymbol{F} boldsymbol{v}^{2}}{boldsymbol{pi}^{2} boldsymbol{t}^{2} boldsymbol{x}}left(text { where } boldsymbol{P}_{boldsymbol{r}}=right. )
Pressure ( F= ) force, ( v= ) velocity, ( t=operatorname{time}, x ) ( = ) distance
State whether true or false: the above
equation is dimentionally correct
A. True
B. False
11
857 6. The percentage error in the above problem is
(a) 7%
(b) 5.95%
(c) 8.95%
(d) 9.85%
11
858 How many order of magnitude are there in one million?
A. 5
B. 4
( c cdot 6 )
D. None of above
11
859 46. The length 1, breadth b, and thickness t of a block of wood
were measured with the help of a measuring scale. The
results with permissible errors (in cm) are
1 = 15.12 +0.01, b = 10.15 +0.01, and t = 5.28 +0.01.
The percentage error in volume up to proper significant
figures is
a. 0.28% b. 0.35% c. 0.48% d. 0.64%
4- Tumolotitre donoitu of material afhad ‘found
11
860 A barometer is faulty. When the true barometer reading are 73 and ( 75 mathrm{cm} ) of Hg, the faulty barometer reads ( 69 mathrm{cm} )
and ( 70 mathrm{cm} ) respectively. What is the total length of the barometer tube?
11
861 34. The position x of a particle at time t is given by
x= (1-e-at), where V, is constant and a > 0. The
dimensions of V, and a are
a. M°LT-1 and T b. M°LT° and T
c. M°LT-1 and LT-2 d. Mºlt-1 and T
11
862 For n moles of gas Vander waal’s equation is ( left(boldsymbol{P}-frac{boldsymbol{a}}{boldsymbol{V}^{2}}right)(boldsymbol{V}-boldsymbol{b})=boldsymbol{n} boldsymbol{R} boldsymbol{T} )
Find the dimensions of a and b, where ( mathrm{P} )
is gas pressure, ( V= ) volume of gas ( T= ) temperature of gas
11
863 The mass and sides of a cube given as ( (10 k g pm 0.1) ) and ( (0.1 m pm 0.01), ) the
relative error in density is:
A . 0.31
B. 0.5
c. 0.62
D. 0.29
11
864 2.
2
2. 42
C. 12
. 100
74. While measuring acceleration due to gravity by a simple
pendulum, a student makes a positive error of 2% in the
length of the pendulum and a positive error of 1% in the
value of time period. His actual percentage error in the
measurement of the value of g will be
a. 3% b. 0%
c. 4% d. 5%
11
865 The sides of a rectangle are ( 7.01 m ) and 12 ( m . ) Taking the significant figures into account, the area of the rectangle
is
B. ( 84.00 m^{2} )
c. ( 84.12 mathrm{m}^{2} )
D. ( 84 m^{2} )
11
866 Planck’s constant has the dimensions
A ( cdot M L^{3} T^{-1} )
B . ( M L^{2} T^{-1} )
( mathbf{c} cdot M L^{6} T^{-1} )
D. ( M L^{8} T^{-1} ).
11
867 6. A student uses a simple pendulum of exactly 1 m length
to determine g, the acceleration due to gravity. He uses a
stop watch with the least count of 1 s for this and records
40 s for 20 oscillations. For this observation, which of the
following statement(s) is(are) true?
a. Error AT in measuring T, the time period, is 0.05 s
b. Error AT in measuring T, the time period, is 1 s
c. Percentage error in the determination of g is 5%
d. Percentage error in the determination of g is 2.5%
(IIT JEE, 2010)
11
868 Ammeter is used to
measure
A. current
B. voltage
c. charge
D. resistance
11
869 For a circuit, ( L, C ) and ( R ) represent the
inductance, capacitance and resistance. Then, the dimensional
formula for ( C^{2} L R ) is
( mathbf{A} cdot[M L T] )
B . ( left[M^{0} L^{0} T I^{0}right] )
c. ( left[M^{2} L^{2} T^{0} I^{0}right. )
D cdot ( left[M^{0} L^{0} T^{3} I^{0}right] )
11
870 The speed of transverse wave ( v ) in a
stretched string depends on tension ( boldsymbol{T} ) in the string and linear mass density (mass per unit length) ( mu . ) Find the relation using method of dimensions.
11
871 If Planck’s constant ( (h), ) surface tension
( (s) ) and moment of inertia ( (I) ) are taken as fundamental quantities, then dimensions of linear momentum ( (p) ) will be given as:
( mathbf{A} cdot h s^{2} I^{1 / 2} )
B . ( h^{1 / 2} s^{1 / 2} I )
c. ( h^{0} s^{1 / 2} I^{1 / 2} )
D. None of these
11
872 2. Given that: y= A sin
r), where y and x are
measured in the unit of length. Which of the following
statements is true?
a. The unit of 2 is same as that of x and A.
b. The unit of 2 is same as that of x but may not be same
as that of A.
c. The unit of c is same as that of 2702.
d. The unit of (ct – x) is same as that of 210 .
11
873 In a meter bridge experiment, we try to
obtain the null point at the middle. This
reduces:
A. systematic error as well as random errors
B. systematic error but not the random error
c. random error but not the systematic error
D. neither systematic error nor the random error
11
874 Count total number of Significant Figures in 3.0800
A. 3
B. 5
( c )
( D )
11
875 9. The decimal equivalent of 1/20 up to three significant
figures is
(a) 0.0500
(b) 0.05000
(c) 0.0050
(d) 5.0 x 10-2
11
876 What is the mass of an object whose weight is 980 N?
( A cdot 980 mathrm{kg} )
B. 98 kg
( c cdot 100 mathrm{kg} )
D. zero
11
877 Which of the following has highest relative density?
A. water
B. oil
c. mercury
D. glass
11
878 One second is defined to be equal to:
A. 1650763.73 periods of krypton clock
B. 652189.63 period of krypton clock
C. 1650755.73 periods of cesium clock
D. 9,19,26,31,770 periods of cesium clock
11
879 Light year is the unit of the
A. distance
B. time
c. speed
D. intensity of light
11
880 69. A liquid drop of density p, radius r, and surface tension
o oscillates with time period T. Which of the following
expressions for T4 is correct?
pr3
d. None of these
11
881 19. Two resistances R = 100 + 32 and R, = 200 + 4 12 are
connected in series. Find the equivalent resistance of the
series combination.
TL:
1
1
11
882 1 femtometre is equivalent to
( mathbf{A} cdot 10^{15} m )
B. ( 10^{-12} m )
( mathbf{c} cdot 10^{-15} m )
D. ( 10^{-9} m )
11
883 Choose the correct answer from the
following
This question has multiple correct options
( A cdot ) An area of one square centimetre is ( 10^{4} ) times greater
than one square metre
B. 1 hour 18 min is equal to 3618 seconds.
C. Sl unit of volume is cubic metres.
D. Metre is the standard unit to measure length
11
884 30. The order of magnitude of 379 is
a. 1
b. 2
c. 3
d. 4
11
885 If ( y ) represents pressure and ( x ) represents velocity gradient, then the dimensions of ( frac{d^{2} y}{d x^{2}} ) are
( mathbf{A} cdotleft[M L^{-1} T^{-2}right] )
B. ( left[M^{2} L^{-2} T^{-2}right] )
( mathbf{c} cdotleft[M L^{-1} T^{0}right] )
D cdot ( left[M^{2} L^{-2} T^{-4}right] )
11
886 A body is just floating on the surface of liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. Then it will
A. come back slowly to its earlier position
B. remain submerged where it is left.
c. sink in liquid
D. come out vigoursly
11
887 We should not use plurals when we write the unit in words.
A. True
B. False
11
888 7. Two full turns of the circular scale of a screw gauge
cover a distance of 1 mm on its main scale. The total
number of divisions on the circular scale is 50. Further.
it is found that the screw gauge has a zero error of
-0.03 mm. while measuring the diameter of a thin
wire, a student notes the main scale reading of 3 mm
and the number of circular scale divisions in line with
the main scale as 35. The diameter of the wire is
(a) 3.38 mm
(b) 3.32 mm
(c) 3.73 mm
(d) 3.67 mm (AIEEE 2008)
11
889 The dimensional formula for magnetic flux is
( mathbf{A} cdotleft[M L^{2} T^{-2} A^{-1}right] )
B ( cdotleft[M L^{3} T^{-4} A^{-2}right] )
c. ( left[M^{0} L^{-2} T^{-2} A^{-2}right] )
D ( cdotleft[M L^{2} T^{-1} A^{2}right] )
11
890 Measuring vessel to measure volume of irregular shaped solid is
A. Measuring Jar
B. measuring bowl
c. Any of these can be used
D. None
11
891 Of the following quatities, which one
has dimensions different from the
remaining three?
A. Energy per unit volume
B. Force per unit area
c. Product of voltage and charge per unit volume
D. Angular momentum
11
892 3. Two quantities A and B have different dimensions.
Which mathematical operation given below is physically
meaningful?
(a) A/B (b) A+B (c) A – B (d) None
11
893 nanometer is ( _{–} ) femtometer.
A ( cdot 10^{5} )
B. ( 10^{text {6 }} )
( c cdot 10^{7} )
D. ( 10^{4} )
11
894 1 по апппопор о соuр ас
20. The dimensional formula for impulse is
21 The dimensional formula for Planck’s constant (1
11
895 Dimensions of impulse are
( mathbf{A} cdotleft[M L T^{-1}right] )
( mathbf{B} cdotleft[M L T^{2}right] )
c. ( left[M T^{-2}right] )
D・ ( left[M L^{-1} T^{-3}right] )
11
896 The ampere, metre and second are ( mathrm{S} )
base units.
State two other SI base units.
11
897 A cube has sides of length ( 1.2 times )
( 10^{-2} m . ) Calculate the volume.
A ( .1 .7 times 10^{-6} m^{3} )
В. ( 1.73 times 10^{-6} m^{3} )
C. ( 1.70 times 10^{-6} m^{3} )
D. ( 1.732 times 10^{-6} mathrm{m}^{3} )
11
898 U. 2I11.2JXU) 52
56. Which of the following product of e, h, u, G (where u is
the permeability) be taken so that the dimensions of the
product are same as that of the speed of light?
a. he-Pu-16°
b. h’eGºju
c. hºe?G-‘u
d. hGe-?uº
7 WILL C11
11
899 3. To determine the Young’s modulus of a wire, the formula is
Y==x ; where L= length, A = area of cross-section of
A AL
the wire, AL = change in length of the wire when stretched
with a force F. The conversion factor to change it from
CGS to MKS system is
(a) 1
(b) 10
(d) 0.01
(c) 0.1
11
11
900 Which of the following time measuring devices is most precise?
A. A wall clock
B. An atomic clock
c. A digital watch
D. stop watch
11
901 12. If there is a positive error of 50% in the measurement of
velocity of a body, then the error in the measurement of
kinetic energy is
(a) 25%
(b) 50%
(c) 100%
(d) 125%
11
902 A physical quantity ( A ) is related to four observable ( a, b, c ) and ( d ) as follows, ( A= ) ( frac{a^{2} b^{3}}{c sqrt{d}}, ) the percentage errors of
measurement in ( a, b, c ) and ( d ) are ( 1 %, 3 % ) ( 2 % ) and ( 2 % ) respectively. What is the percentage error in the quantity ( boldsymbol{A} ) ?
A . ( 12 % )
B . ( 7 % )
c. ( 5 % )
D. 14%
11
903 A metre scale weighs 50 grams and carries 20 grams at one end, the scale balances when it is suspended at a
distance ( x ) from other endpoints. Then ( x )
is equal to?
A . ( 35.7 mathrm{cm} )
в. 64.3 ст
c. ( 14.3 mathrm{cm} )
D. ( 50 mathrm{cm} )
11
904 Calculate the mass of a body in tonnes
whose volume is ( 2 mathrm{m}^{3} ) and ( mathrm{R.D} ) is 5.2
11
905 If the error in measurements of mass
and velocity is ( 1 % ) each then error in measurement of kinetic energy is:
11
906 A physical quantity ( x ) is calculated from
the relation ( boldsymbol{x}=boldsymbol{a}^{3} boldsymbol{b}^{2} / sqrt{boldsymbol{c} boldsymbol{d}} ). Calculate
percentage error in ( x, ) if ( a, b, c ) and ( d ) are measured respectively with an error of ( 1 %, 3 %, 4 % ) and ( 2 % )
A. ( 12 % )
в. ( 22 % )
c. ( 2 % )
D. ( 0.2 % )
11
907 If ( a, b, c ) are the percentage errors in the measurement of ( A, B ) and ( C, ) then the
percentage error in ABC would be
approximately
A ( . a b c )
B . ( a+b+c )
c. ( a b+b c+a c )
D. ( frac{a}{b}+frac{b}{c}+frac{c}{a} )
11
908 The period of oscillation of a simple pendulum is ( T=2 pi sqrt{frac{L}{g}} . ) Measured of ( L ) is ( 20.0 mathrm{cm} ) known to ( 1 mathrm{mm} ) accuracy
and time for 100 oscillations of the
pendulum is found to be 90 s using a
wrist watch of ( 1 s ) resolution. The
accuracy in the determination of ( g ) ?
A . ( 2.5 % )
в. ( 2.7 % )
c. ( 2 % )
D. 3%
11
909 Count total number of S.F. in 300.00
A. 5
B. 6
( c cdot 8 )
D. 9
11
910 Atto is used as prefix in SI system. If
true enter 1 else enter 0
11
911 The diameter of a wire as measured by
screw gauge was found to be
2.620,2.625,2.628 and ( 2.626 mathrm{cm} )
Calculate percentage error.
11
912 micrometer is ( quad ) kilometer.
A ( cdot 10^{-9} )
B. ( 10^{-8} )
( mathbf{c} cdot 10^{-10} )
D. ( 10^{8} )
11
913 22. The dimensions of calorie are 11
914 8. A student performs an experiment for determination of
1 40²2
-1,L=1 m, and he commits an error of AL. For
g
=
I
2
The takes the time of n oscillations with the stop watch
of least count AT. For which of the following data, the
measurement of g will be most accurate?
a. AL = 0.5, AT = 0.1, n = 20
b. AL = 0.5, AT = 0.1, n = 50
AL = 0.5, AT = 0.01, n = 20
d. AL = 0.5, AT = 0.05, n = 50 (IIT JEE, 2006)
11
915 The Sl unit of weight is
( mathbf{A} cdot ) кgf
B. Gf
( c cdot N )
D. None of these
11
916 1. The dimensions of a are
a. ML T2
b. MC-T2
d. L6
c. 13
11
917 A physical quantity P is related to four observables ( a, b, c ) and ( d ) as follows:
( mathrm{P} boldsymbol{a}^{3} boldsymbol{b}^{2} / sqrt{boldsymbol{c}} mathrm{d} )
The percentage errors of measurement in ( a, b, c ) and ( d ) are ( 1 %, 3 %, 4 % ) and ( 2 %, ) respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be ( 3.763, ) to what value
should you round off the result?
11
918 65. Assuming that the mass m of the largest stone that can be
moved by a flowing river depends upon the velocity v of
the water, its density p, and the acceleration due to gravity
g. Then m is directly proportional to
3. i b. vt c. y do vo l an
1
11
919 The value of ( sqrt{2} ) in correct significant
digits is :
A .1 .414
B. 1.4
( c cdot 1.0 )
( D )
11
920 The weight of an object is zero at:
A. a height equal to half of the radius of earth
B. the center of the earth
C . the equator
D. both (1) and (2)
11
921 The reference standard used for the
measurement of a physical quantity is called:
A. standard quality
B. Dimension
c. constant
D. Unit
11
922 Each side of a cube is measured to
7.203 ( mathrm{m} ). Find the volume of the cube up
to appropriate significant figures.
11
923 Match the following: 11
924 In the equation ( y=A sin (omega-K x) )
obtain the dimensional formula of ( omega )
and K.Given ( x ) is distance and ( t ) is time.
11
925 If we weigh a given substance five times, and get 5 kg each time, then your measurement is very
A. Accurate
B. Precised
c. Accurate and Precised
D. cannot be judged
11
926 State whether weight is a scalar or vector quantity? 11
927 Density is a physical quantity.
A. fundamental
B. derived
c. semi-derived
D. semi-fundamental
11
928 The value of gravitation constant is ( boldsymbol{G}=mathbf{6 . 6 7} times mathbf{1 0}^{-mathbf{1 1}} boldsymbol{N}-boldsymbol{m}^{2} / boldsymbol{k g}^{2} ) in SI
units. Convert it into CGS system of
units.
A. Thus, value of G in CGS system of units is 6.67 x ( 10^{-8} ) dyne ( c m^{2} / g^{2} )
B. Thus, value of G in CGS system of units is ( 6.67 times ) ( 10^{-9} ) dyne ( c m^{2} / g^{2} )
c. Thus, value of G in CGS system of units is 6.67 x ( 10^{-7} ) dyne ( c m^{2} / g^{2} )
D. Thus, value of G in CGS system of units is 6.67 x ( 10^{-10} ) dyne ( c m^{2} / g^{2} )
11
929 Fill in the blanks:
A quantity which can be completely represented by magnitude alone is called
11
930 Assertion
The Sl unit of weight is Newton.
Reason
Weight is the force of gravity with which
a body is attracted towards the earth.
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
931 Solve with due regard to significant figures: ( frac{5.42 times 0.6753}{0.085} ) 11
932 Suppose, the torque acting on a body is ( operatorname{given} ) by ( boldsymbol{tau}=boldsymbol{K} boldsymbol{L}+boldsymbol{M} boldsymbol{I} / boldsymbol{w} . ) Where ( boldsymbol{L}= )
angular momentum, ( I= ) moment of
inertia, ( boldsymbol{w}= ) angular speed. The
dimensional formula for ( boldsymbol{K} boldsymbol{M} ) is same
as that for:
A ( cdot ) time ( ^{2} )
B . time ( ^{4} )
( mathrm{c} cdot operatorname{time}^{-2} )
D. time ( ^{-4} )
11
933 picometer is centimeter
A ( cdot 10^{-8} )
B. ( 10^{-9} )
c. ( 10^{-10} )
D. ( 10^{10} )
11
934 Students ( A, B ) and ( C ) measure the diameter
of a copper ball using the same screw gauge. A takes 5 readings, ( mathrm{B} ) takes 9 readings and C takes 8 readings. The measured value will be most accurate for
( A cdot B )
B. A
( c cdot c )
D. all
11
935 Write down the number of significant figures in the following.
6428
A. four
B. three
c. ( t w o )
D. one
11
936 Find the dimensional formulae of the
following quantities:
1. the universal constant of gravitational
( G )
2. the surface tension ( S )
3. the thermal conductivity ( k ) and
4. the coefficient of viscosity ( eta )
11
937 The frequency of vibration (v) of a string may depend upon length (I) of the string, tension (T) in the string and mass per unit length (m) of the string. Use method of dimensions for
establishing the formula for frequency
11
938 15. Dimensional formula for latent heat is 11
939 The random error in the arithmatic
mean of 10 observations is ( k . ) Then
random error in arithmatic mean of 25
observations would be
A. ( 0.1 k )
( k )
в. ( 0.4 k )
( c .2 .5 k )
D. ( 1.25 k )
11
940 The prefix ‘milli’ denotes the factor ( 10^{-x} )
( m )
find ( times ? )
11
941 Each side of a cube is measured to be
( 5.402 mathrm{cm} . ) Find the total surface area
and volume of the cube in appropriate significant figures.
11
942 Angular displacement is:
( A ). a scalar
B. a vector
c. neither ( (a) ) nor ( (b) )
D. either ( (a) ) or ( (b) )
11
943 d.
JW
U.
170
.
0
0
54. An experiment measures quantities a, b, and c, and then
X is calculated from X =-
a11262
3. If the percentage errors
in a, b, and c are 1%, +3%, and +2%, respectively, then
the percentage error in X can be
a. +12.5%
b. +7%
c. +1%
d. +4%
11
944 Explain S.I units 11
945 1 MeV is equal to
( mathbf{A} cdot 1.6 times 10^{13} )Joules
B . ( 1.6 times 10^{13} ) cal.
C ( .1 .6 times 10^{13} ) ergs
D. None of these
11
946 If the mass of the body on the surface of the earth is ( 50 k g, ) its mass at the
centre of the earth is:
A. zero
B. More than ( 50 mathrm{kg} )
c. Less than ( 50 mathrm{kg} )
D. Equal to ( 50 mathrm{kg} )
11
947 An infinite long plate has surface
charge density
sigma As shown in the figure, a point
charge ( q ) is moved from ( A ) to ( B ) Net work
done by electric field is:
11
948 How many significant figures are there
in ( 0.30100 ? )
11
949 7. If pressure P, velocity Vand time T are taken as fundamental
physical quantities, the dimensional formula of force is
(a) PV2T2 (b) p-lv2T-2 (c) PVT2 (d) plVT?
11
950 Which of the following is the smallest unit?
A. millimetre
B. angstrom
c. fermi
D. metre
11
951 Find symbols have standard meanings.
(a) electric field ( mathrm{E} )
(B) magnetic field B and
(c) magnetic permeability ( eta_{0} ) The relevant equation are
11
952 A light year is the unit of :
A. time
B. distance
c. intensity of light
D. frequency
11
953 The mass of a planet is 4 times while its radius is 8 times that of the earth. If the weight of an object is ( 640 mathrm{N} ) on earth, what will be its weight on the planet?
A. ( 40 mathrm{N} )
в. 80 N
( c cdot 160 N )
D. 120 N
11
954 The angle subtended at the centre of a
circle by an arc whose length is equal to the diameter of the circle is:
A . radian
B. 2 radian
c. ( pi ) radian
D. ( pi / 2 ) radian
11
955 Assertion
Density of a substance is the ratio of
mass of the substance to its volume
Reason
Relative density is the ratio of density of
substance to the density of water at ( 4^{circ} mathrm{C} )
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
956 Which one exception, each of the following units can be used to express mass. What is the exception?
A. Newton
B. Gram
c. kilogram
D. ( N s^{2} / m )
11
957 The symbol for a unit which is not named in the honour of some scientist
is written in
A. Lower initial letter
B. Initial capital letter
c. Lower letter
D. All
11
958 Instrument used to measure the
temperature is
A. protractor
B. stethoscope
c. thermometer
D. none of these
11
959 How much positive and negative charge
is there in a cup of water?
11
960 The ratio of the values in SI units to
values in CGS units of density is
( mathbf{A} cdot 10^{3}: 1 )
B ( cdot 10^{2}: 1 )
( mathbf{c} cdot 10^{-2}: 1 )
D. ( 10^{-3}: 1 )
11
961 The mass of a full bottle of cooking oil is
( 1.30 k g )
When exactly half of the oil has been used, the mass of the bottle plus the
remaining oil is 0.90 kg.

What is the mass of the empty bottle?
A. ( 0.40 mathrm{kg} )
B. ( 0.50 mathrm{kg} )
c. ( 0.65 mathrm{kg} )
D. ( 0.80 mathrm{kg} )

11
962 When the number 0.046508 is reduced
to 4 significant figures, then it becomes
A . 0.0465
B . ( 4650.8 times 10^{-5} )
c. ( 4.651 times 10^{-2} )
D. ( 4.650 times 10^{-2} )
11
963 In resonance tube exp. we find ( l_{1}= )
( 25.0 mathrm{cm} ) and ( l_{2}=75.0 mathrm{cm} . ) If there is no
error in frequency, what will be maximum permissible error in speed of
sound. (Take ( left.f_{0}=325 H zright) )
( boldsymbol{V}=mathbf{2} boldsymbol{f}_{0}left(boldsymbol{l}_{2}-boldsymbol{l}_{1}right) )
A. ( v=(329 pm 1.3) mathrm{m} / mathrm{s} )
B. ( v=(326 pm 1.3) mathrm{m} / mathrm{s} )
c. ( v=(325 pm 1.4) mathrm{m} / mathrm{s} )
D. ( v=(325 pm 1.3) mathrm{m} / mathrm{s} )
11
964 Match the following:
( A cdot A-r, B-s, C-p )
D-q, ( E-L )
1, E-U ( D-q )
( B cdot A-S, B-r, C-p, )
( C cdot A-r, B-S, C-u, D-q, E-p )
D. A-q, B-s, C-p, D-r ( E-L )
11
965 The Richardson equation is given by ( boldsymbol{I}=boldsymbol{A} boldsymbol{T}^{2} boldsymbol{e}^{frac{-B}{k T}} . ) The dimensional formula
for ( A B^{2} ) is same as that for:
A ( cdot I T^{-2} )
в. ( k ) Т
( c cdot I k^{2} )
D. ( frac{I k^{2}}{T} )
11
966 In an experiment, the refractive index of glass was observed to be
( mathbf{1 . 4 5}, mathbf{1 . 5 6}, mathbf{1 . 5 4}, mathbf{1 . 4 4}, mathbf{1 . 5 4}, mathbf{1 . 4 4}, mathbf{1 . 5 4} )
and ( 1.53 . ) Calculate mean value of refractive index
11
967 Which one of the following statements
İs incorrect?
A. Direct and indirect methods are used for the
measurement of physical quantities.
B. Scientific notation and the prefixes are used to simplify numerical computation.
C. A dimensionally correct equation need not be a correct equation.
D. The Sl units is based on six base units.
11
968 Two resistances are expressed as
( boldsymbol{R}_{1}(mathbf{4} pm mathbf{0 . 5} %) boldsymbol{Omega} ) and ( boldsymbol{R}_{2}(mathbf{1 2} pm mathbf{0 . 5} %) boldsymbol{Omega} )
The net resistance when they are
connected in series with percentage
error is:
(In series ( left.boldsymbol{R}=boldsymbol{R}_{1}+boldsymbol{R}_{2}right) )
A . ( (16 pm 0.5 %) Omega )
B. ( (16 pm 6.25 %) Omega )
c. ( (16 pm 22 %) Omega )
D. ( (16 pm 2.2 %) Omega )
11
969 vom u unu
6. Given that T stands for time period and I stands for the
length of simple pendulum. If g is the acceleration due to
gravity, then which of the following statements about the
relation Tº = (l/g) is correct?
a. It is correct both dimensionally as well as numeri-
cally.
b. It is neither dimensionally correct nor numerically.
c. It is dimensionally correct but not numerically.
d. It is numerically correct but not dimensionally.
11
970 Which of the following is a fundamental
unit?
A. Ampere
B. Newton
c. volt
D. onm
11
971 Dyne – second is the unit of:
A. Force
B. Momentum
c. Energy
D. Power
11
972 The S.I. unit of velocity is
( mathbf{A} cdot k m h^{-1} )
B. ( m ) min ( ^{-1} )
c. ( k m ) min ( ^{-1} )
( mathbf{D} cdot m s^{-1} )
11
973 The Sl unit of electron mobility is :
A ( . M^{2} S^{-1} V-1 )
В. ( =m^{2} s^{-1} V^{-1} )
( mathbf{c} cdot m s^{-1} V )
D. ( m^{2} s^{-2} V )
11
974 5. A suitable unit for gravitational constant is
(a) kg-m sec-
(b) Nm’ sec
(c) N m² kg 2
(d) kg m sec
CT
11
975 If error in measurement of radium of a
sphere is ( 1 %, ) what will be the error in
measurement of volume?
A . ( 1 % )
B. ( frac{1}{3} % )
( c .3 % )
D. None of these
11
976 In the equation ( y=A sin left[k t-frac{x}{lambda}right], ) the dimensional formula for ( k ) is
A ( cdot M^{0} L^{0} T^{-1} )
B . ( M^{0} L^{0} T^{0} )
c. ( M^{0} L T^{0} )
D. ( M L^{0} T^{0} )
11
977 The addition of two numbers ( 6.75 times 10^{3} )
( mathrm{cm} ) and ( 4.52 times 10^{2} mathrm{cm} ) with regard to
significant figures is:
A ( cdot 7.20 times 10^{3} mathrm{cm} )
В. ( 7.20 times 10^{3} mathrm{mm} )
c. ( 7.20 times 10^{4} mathrm{cm} )
D. None of these
11
978 In a burette, the zero mark on the
graduation scale is near its mouth.
A. True
B. False
11
979 13. The dimensional formula for resistivity of conductor is
a. [M L?T-2A-2] b. [M LT-3A-2)
c. [ML-2T-2A²) d. [M LT-2A-31
11
980 A physical quanity ( P ) is releated to four
observation ( a, b, c ) and ( d ) as follows ( P= )
( a^{3} b^{3} / sqrt{c d T h e} ) percentage errors of
measurement in ( a, b, c ) and ( 1 %, 3 %, 4 % )
and ( 2 % ) repectively. What is the
percentage erros in quanity ( P ) ? If the
value of ( boldsymbol{P} ). Calculated using the above
relations turns out to +ve ( 3.763, ) to what value you should round off the result?
11
981 Unit of plane angle is
A. Radian
B. Steradian
c. Degree
D. Celcius
11
982 A century has
A. 100 years
B. 100 months
c. 100 seconds
D. 100 weeks
11
983 Dimensions of ‘ohm’ are same as that
of:
(Given ( : h ) is Planck’s constant and ( e ) is
charge)
( A cdot frac{h}{e} )
в. ( frac{h^{2}}{e} )
( c cdot frac{h}{e^{2}} )
D. ( frac{h^{2}}{e^{2}} )
11
984 7. The %error in measurement of resistivity is mostly
effected by %error in
(a) length measurement
(b) voltage measurement
(c) current measurement
(d) diameter measurement
11
985 44. If the velocity of light C, the universal gravitational
constant G, and Planck’s constant h are chosen as
fundamental units, the dimensions of mass in this system
are
a. h1/21/2G-1/2
b. h-C-G
c. hCG-1
d. hCG
2.4 W. hCG
11
986 The percentage error in a measurement
of ( 6 m m text { is } 0.1 % text { , the error is (in } m m) )
A . 0.6
B. 0.06
c. 0.006
D. 0.001
11
987 Four charges are placed at the
circumference of the dial of a clock as
shown in figure. If the clock has only
hour hand, then the resultant force on a
positive charge ( q_{0} ) placed at the centre,
points in the direction which shows the
time as :-
A . 1: 30
B. 7:30
( c cdot 4: 30 )
D. 10: 30
11
988 The thickness of a metal sheet is
measured to be ( 326 m m ). Express its
order of magnitude in ( mathrm{mm} )
A ( cdot 10^{circ} )
B. ( 10^{text {। }} )
( c cdot 10^{2} )
D. ( 10^{3} )
11
989 5. The sum of the numbers 436.32, 227.2 and 0.301 in
appropriate significant figures is
(a) 663.821
(c) 663.8
(d) 663.82
(b) 664
11
990 A physical quantity ( x ) is calculated from the relation ( x=frac{a^{2} b^{3}}{c sqrt{d}} . ) If the percentage
error in ( a, b, c ) and ( d ) are ( 2 %, 1 %, 3 % ) and ( 4 % ), respectively, what is the percentage
error in ( x ) ?
11
991 The refractive index ( (mu) ) of glass is found to have the values
1.49,1.50,1.52,1.54 and 1.48
Calculate the absolute error in each
measurement.
11
992 The area of rectangle of size ( 1.23 mathrm{cm} times )
( 2.345 mathrm{cm} ) is ?
A. ( 2.88 c m^{2} )
2
B . ( 2.884 c m^{2} )
( mathrm{c} cdot 2.9 mathrm{cm}^{2} )
D . ( 2.88435 mathrm{cm}^{2} )
11
993 25. The dimensions of intensity of wave are
a. [M LT-3]
b. [MLºT-31
c. [M L-2 T-3]
.
d. [MºĽT]
26
The dimanaiane af
1
11
994 ( 10 mathrm{kg} ) of a metals melted and recast into a cylinder of diameter ( 6 mathrm{mm} ) and ( 25 mathrm{cm} )
long. Find the density of the cylinder. If this cylinder is again melted and recast into 7 equal sized cubes find the density
of each cube. Whet do you infer about densities found?
11
995 In some observations, value of ‘g’ are
coming as 9.81,9.80,9.82,9.79,9.78
9.84,9.79,9.78,9.79 and ( 9.80 m / s^{2} )
Calculate absolute errors and
percentage error in ( mathfrak{g} )
A ( cdot quad ) ‘g’ ( =(9.80 pm 0.014) mathrm{m} / mathrm{s}^{2} )
B. ‘g’= (9.8 ±0.14 ) ( m / s^{2} )
c. ( operatorname{tg}^{prime}=(9.8 pm 0.0014) m / s^{2} )
D. ‘g’= (9.8000 ( pm 0.00014) mathrm{m} / mathrm{s}^{2} )
11
996 Round off following number upto four significant figures
45.689
A . 45.689
B. 45.69
c. 45.68
D. 45.7
11
997 If in the formula ( boldsymbol{X}=mathbf{3} boldsymbol{Y} boldsymbol{Z}^{2}, ) the
dimensions of ( X ) and ( Z ) are those of the
capacitance and magnetic induction, then the dimensions of Y are:
A . ( M^{-3} L^{-2} T^{8} A^{4} )
B. ( M^{-3} L^{-2} T^{4} A^{4} )
( mathbf{c} cdot M^{-3} L^{-2} T^{-4} A^{-4} )
D. ( M^{-3} V^{-2} T^{-8} A^{-4} )
11
998 The order of magnitude of 147 is
( A cdot 1 )
B. 2
( c .3 )
D. 4
11
999 How can you minimize backlash error? 11
1000 Subtract ( 3.2 times 10^{-6} ) from ( 4.7 times 10^{-4} )
with due regard to significant figures.
В. ( 7 times 10^{-4} )
c. ( 5.7 times 10^{-4} )
D. ( 4.7 times 10^{-5} )
11
1001 A body of mass ( m=3.513 mathrm{kg} ) is moving
along the ( x ) -axis with a speed of
( mathbf{5 . 0 0 m s}^{-1} . ) The magnitude of its momentum is recorded as:
A . 17.56 kgms ( ^{-1} )
в. 17.57 kgms( ^{-1} )
c. ( 17.6 mathrm{kgms}^{-1} )
D. 17.565 kgms( ^{-1} )
11
1002 72. The length of a strip measured with a meter rod is 10.0 cm.
Its width measured with a vernier callipers is 1.00 cm. The
least count of the meter rod is 0.1 cm and that of vernier
callipers is 0.01 cm. What will be the error in its area?
a. 0.01 cm
b. +0.1 cm2
C. 0.11 cm
d. +0.2 cm2
11
1003 The Sl unit of coefficient of mutual
inductance of a coil is
A. henry
B. volt
c. farad
D. weber
11
1004 If kinetic energy’ ( K ), velocity’ ( v ) ‘ and
time ‘T’ are chosen as the fundamental
units, the formula for surface tension ( S )
( = )
( (A text { is a constant }) )
( ^{mathbf{A}} cdot frac{v^{2} K^{2}}{A K} )
в. ( frac{v^{2}}{A K T} )
c. ( frac{A K T^{2}}{v^{2}} )
D. ( frac{A K}{v^{2} T^{2}} )
11
1005 Differentiate between the scalar and
vector quantities, giving two examples
of each.
11
1006 Write ( S I ) units of luminous intensity
and temperature
11
1007 Write S.I. unit of charge
A .
B. A
C. ( mathrm{N} mathrm{m}^{2} )
D. None of the above
11
1008 Which of the following systems of units is not based on units of mass, length and time alone?
A. s
в. мкя
c. cas
D. FPS
11
1009 The diameter of a wire as measured by
a screw gauge was found to be ( 1.002 mathrm{cm}, 1.004 mathrm{cm} ) and ( 1.006 mathrm{cm} . ) The
absolute error in the third reading is:
A ( .0 .002 mathrm{cm} )
B. ( 0.004 mathrm{cm} )
c. zero
D. ( 1.002 mathrm{cm} )
11
1010 Any unit which can be obtained by the combination of one or more
fundamental units is called
A. Fundamental unit
B. Scale
c. Derived unit
D. standard unit
11
1011 A given quantity has both magnitude and direction. Is it necessarily be a vector? Justify. 11
1012 10. The velocity of a freely falling body changes as gPh9 where
g is acceleration due to gravity and h is the height. The
values of p and q are
(a) 1,
(b) 1 1
(b) 2.2
(d) 1,1
21.
11.
d
11
1013 The paint in a certain container is sufficient to paint an area equal to
( 9.375 m^{2} . ) How many bricks of
dimensions ( 22.5 times 10 times 7.5 c m ) can be
painted out of this container?
11
1014 kilometer is decimeter.
A ( cdot 10^{4} )
B . ( 10^{5} )
( c cdot 10^{3} )
D. ( 10^{6} )
11
1015 4. Which pair has the same dimensions?
(a) Work and power
(b) Density and relative density
(c) Momentum and impulse
(d) Stress and strain
The dimensional formula for imnulce is same
11
1016 ( g c m s^{-2} ) is also known as
A. newton
B. erg
c. pascal
D. dyne
11
1017 Match the Following:
begin{tabular}{lll|l}
& Column – I & & Column \
& & -II \
A & Weight & p & Scalar \
B & Mass & q & Vector \
C & Force & r & kilogram \
D & Quantity of matter in a body & s & Kgwt (or) kgf
end{tabular}
( A cdot A-q, s ; B-p, r ; C-q, s ; D-p, r )
B. A-r,s; B-p,q; C-q,s; D-p,r
C. ( A-q, s ; B-p, r ; C-q, r ; D-p, s )
D. A-q,s; B-p,s; C-q,r; D-p,
11
1018 21. If force F, acceleration a, and time T are taken as the
fundamental physical quantities, the dimensions of length
on this system of units are
a. FAT b. FAT c. FT d. AT?
2
11
1019 Using the concept of force between two
infinitely long parallel current carrying conductors, define one ampere of
current
11
1020 Assertion
The precision of a measurement depends on least count of measuring instrument.
Reason
Smaller the least count greater is number of significant figures in
measurement value
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
1021 Fill in the blank:
The last digit in the measurement gives
the first
A. certain
B. significant
c. uncertain
D. insignificant
11
1022 Find the dimensions of pressure. 11
1023 The force with which the earth attracts
a body is called its mass. True or false.
A. True
B. False
11
1024 Convert the given measurement into the bigger unit. Then, multiply by the second number and find the products. ( 7 k m 63 m ) and 4 11
1025 The respective number of significant
figures for the numbers 23.023,0.0003
and ( 2.1 times 10^{-3} ) are
A. 5,1,2
B. 5,1,5
( c cdot 5,5,2 )
D. 4,4,2
11
1026 12. Force F is given in terms of time t and distance x by
F = A sin Ct + B cos Dx. Then the dimensions of A/B and
CID are
a. [MºLºTº], [M°LOT-1
b. [MLT-2), [MºL-‘T”]
c. [Mºlºtº], [MºLT-11
d. [MºLT-‘], [M°C°T°)
11
11
1027 Students ( A, B ) and ( C ) measure the
diameter of a wire using three different screw gauges of least count 0.01
( mathrm{cm}, 0.05 mathrm{cm} ) and ( 0.001 mathrm{cm} ) respectively. Each one makes 10 measurements.The
measurements will be more precise for
( A cdot A )
B. B
( c cdot c )
D. all
11
1028 ( mathbf{5 8 0 0} boldsymbol{A} ) in nm will be?
A. 58
B. 5.8
( c .580 )
D. 0.58
11
1029 A physical quantity of the dimensions of mass that can be formed out of ( c, G ) and ( frac{e^{2}}{8 pi varepsilon_{0}} ) is ( (c text { is velocity of light, } G ) is
universal constant of gravitation and ( e )
is charge, ( left.varepsilon_{0} text { is electrical permittivity }right) )
( ^{mathbf{A}} cdotleft[G frac{e^{2}}{8 pi varepsilon_{0}}right]^{frac{1}{2}} )
( ^{mathbf{B}} cdot_{c^{0}}left[frac{G e^{2}}{8 pi varepsilon_{0}}right]^{2} )
( c cdotleft[frac{e^{2}}{G 8 pi varepsilon_{0}}right]^{frac{1}{2}} )
( c^{0}left[frac{G e^{2}}{8 pi varepsilon_{0}}right]^{frac{1}{2}} )
11
1030 The length I, breadth b, and thickness t of a block of wood were measured with
the help of a measuring scale. The results with permissible errors (in cm )
are
( l=15.12+_{0} .01, b=10.15+0 )
( .01, ) andt ( =5.28+0.01 )
The percentage error in volume up to proper significant figures is
A. ( 0.28 % )
B. ( 0.35 % )
c. ( 0.48 % )
D. ( 0.64 % )
11
1031 Which of the following physical quantities has same unit in all the
three system of units?
A . Mass
B. Length
c. Time
D. None of these
11
1032 Modulus of Elasticity is dimensionally equivalent to:
A. Stress
B. Surface tension
c. Strain
D. coefficient of viscosity
11
1033 dt
3. In the relation” = 20 sin(ot+.), the dimensional
formula for ot + Po is
a. MLT b. MLTºc. ML°T° d. Mºl°T°
11
1034 3. Error in the measurement of radius of a sphere is 1%. The
error in the calculated value of its volume is
(a) 1% (b) 3% (c) 5% (d) 7%
11
1035 The dimension of stopping potential ( V_{0} ) in photoelectric effect in units of Planck’s constant ‘h’, speed of light ‘c’
and Gravitational constant ‘G’ and
ampere ( A ) is:
A ( cdot h^{-2 / 3} c^{-1 / 3} G^{4 / 3} A^{-1} )
B ( cdot h^{2} G^{3 / 2} c^{1 / 3} A^{-1} )
c. ( h^{0} c^{5} G^{-1} A^{-1} )
D. ( h^{1 / 3} G^{2 / 3} c^{1 / 3} A^{-1} )
11
1036 Error due to eye vision is termed as:
A. climax error
B. sight error
c. parallax error
D. visional error
11
1037 If the unit of mass, length and time be each doubled,then how the unit of power will change. 11
1038 11. The equation (P+ 2 (v – b) constant. The unit of a is
(a) Dyne x cm (b) Dyne x cm
(c) Dyne/cm3
(d) Dyne/cm2
11
1039 What is the value of 1 fermi in ( m ? )
A ( cdot 10^{-3} )
3
B. ( 10^{-6} )
( c cdot 10^{15} )
D. ( 10^{-15} )
11
1040 The scalar quantity among the following
is
A. weight of body
B. temperature gradient
c. elementary area
D. magnetic field strength
11
1041 8. Temperature can be expressed as a derived quantity in
terms of any of the following
(a) Length and mass
(b) Mass and time
(c) Length, mass and time
(d) None of these
11
1042 For measuring time in sports events
like sprinting, milisecond( (boldsymbol{m s}) ) is a commonly used unit of time. 1 ms ( =? )
( mathbf{A} cdot 10^{-12} s )
B. ( 10^{-9} s )
( mathbf{c} cdot 10^{-3} s )
D. None of these
11
1043 ( mathbf{5 8 0 0} boldsymbol{A}=mathbf{5 . 8} times mathbf{1 0}^{-boldsymbol{x}} boldsymbol{m} . ) Find the value
of ( boldsymbol{x} )
11
1044 If the unit of length is doubled the
numerical value of Area will become
times its original value.
A ( cdot frac{1}{2} )
B. ( frac{1}{4} )
( c cdot 2 )
D. 4
11
1045 1. A particle of mass m is located in a region where its
potential energy [U(x)] depends on the position x as
Potential Energy [U(x)]=– -here a and b are positive
constants
(i) Write dimensional formula of a and b
(ii) If the time period of oscillation which is calculated
from above formula is stated by a student as T = 4ta
xx
ma , check whether his answer is dimensionally
132
correct.
11
1046 Which among the following is the smallest prefix?
A. mill
B. nano
c. fermi
D. deci
11
1047 Sl unit of the angular velocity is
( A cdot m / s )
B. rad
( c cdot operatorname{rad} / mathrm{s} )
D. m/rad
11
1048 10. A screw gauge gives the following reading when used to
measure the diameter of a wire.
Main scale reading: 0 mm
Circular scale reading: 52 divisions
Given that 1 mm on main scale corresponds to 100
divisions of the circular scale.
The diameter of wire from the above data is:
(a) 0.52 cm
(b) 0.052 cm
(c) 0.026 cm
(d) 0.005 cm (AIEEE 2011)
11
1049 3. Which of the following does not have the same dimensional
formula as that for RT?
a. PV
b. Pb
ab
c. V²
V2
11
1050 The unitless quantity is:
A. velocity gradient
B. pressure gradiant
C. displacement gradient
D. force gradient
11
1051 An iron cylinder of radius ( 1.4 mathrm{cm} ) and
length ( 8 mathrm{cm} ) is found to weigh ( 369.6 mathrm{g} )
Calculate the density of iron.
A ( cdot 7500 mathrm{kg} / mathrm{m}^{3} )
B. ( 7500 g / c m^{3} )
c. ( 7500 k g / c m^{3} )
D. None of the above
11
1052 Calculate the area enclosed by a circle
of radius ( 0.56 mathrm{m} ) to the correct number
of significant figures.
11
1053 A block of wood of mass ( 24 mathrm{kg} ) floats on
water. The volume of wood is ( 0.032 m^{3} )
Find the density of wood.(Density of
water ( left.=1000 mathrm{kg} m^{-3}right) )
11
1054 Pico is used as prefix in SI system. True ( =1, ) false ( =0 ) 11
1055 The equation of a wave is given by ( Y= ) ( 4 sin omegaleft(frac{x}{v}-kright) ) where ( omega ) is the angular
velocity and ( v ) is the linear velocity. The
dimensions of ( k ) is ( ? )
( A cdot[L T] )
в. ( [T] )
( mathbf{c} cdotleft[T^{-1}right] )
D・[T’]
11
1056 The density of mercury is ( 13.6 g m / c c ) Convert it into S.I. units:
A ( cdot 13.6 times 10^{3} k g / m^{3} )
B. ( 13.6 times 10^{2} k g / m^{3} )
c. ( 13.6 times 10^{4} k g / m^{3} )
D. ( 13.6 times 10^{5} mathrm{kg} / mathrm{m}^{3} )
11
1057 Illustration 1.4 In CGS system the magnitude of the force is
100 dynes. In another system where the fundamental physical
quantities are kilogram, meter, and minute, find the magnitude
of the force.
11
1058 A motorboat, whose speed in ( 15 mathrm{km} / mathrm{hr} )
in still water goes ( 30 mathrm{km} ) downstream
and comes back in a total of 4 hours 30
minutes. The speed of the stream (in ( mathrm{km} / mathrm{hr}) ) is:
11
1059 Newton used the phrase ‘quantity of motion’ for
A. Momentum
B. Force
c. Acceleration due to gravity
D. None of these
11
1060 1. L, C, and R represent the physical quantities inductance,
capacitance, and resistance, respectively. The combinations
which have the dimension of frequency are
a. 1/RC
b. RIL
c. 1/VLC
d. CIL (IIT JEE, 1984)
11
1061 Linear momentum and angular
momentum have the same dimensions
in:
A. mass and length
B. length and time
c. mass and time
D. mass, length and time
11
1062 The volume ( V ) of a liquid crossing through a tube is related to the area of cross-section ( A ), velocity ( v ) and time ( t ) as
( boldsymbol{V} propto boldsymbol{A}^{boldsymbol{a}} boldsymbol{v}^{b} boldsymbol{t}^{c} . ) Which of the following is
correct given that ( a neq 1 ? )
A. ( a neq b ) and ( b neq c )
B. ( a=b ) and ( b=c )
c. ( a neq b ) and ( b=c )
D. ( a=b ) and ( b neq c )
11
1063 The most basic rule of dimensional
analysis is that of dimensional homogeneity. Only commensurable quantities may be
A. compared
B. equated
c. added or subtracted
D. all of the above
11
1064 Cut TLS SUCOUW
17. Calculate the percentage error in specific resistance,
p=rR/I, where r = radius of wire = 0.26 + 0.02 cm,
1 = length of wire = 156.0 + 0.1 cm, and R = resistance
of wire = 64+2 2.
L
11
1065 ( L, C ) and ( R ) represents the physical quantities, inductance, capacitance and resistance respectively. The
combinations which have the
dimensions of frequency are:
A. ( 1 / R C )
в. ( R C / L )
c. ( 1 / sqrt{L R C} )
D. ( C / L )
11
1066 Dimensions of ( frac{1}{mu_{o} epsilon_{o}}, ) where symbols
have their usual meaning, are
A ( cdotleft[L^{-1} Tright] )
B . ( left[L^{-2} T^{2}right]^{2} )
c. ( left[L^{2} T^{-2}right] )
D・ ( left[L T^{-1}right] )
11
1067 8
=
2. A student performs an experiment for determination of
( 47²e)
-, L = lm, and he commits an error of AL.
T2
For T, he takes the time of n oscillations with the stop
watch of least count At and he commits a human error of
0.1 sec. For which of the following data, the measurement
of g will be most accurate?
(a) AL = 0.5, At = 0.1, n = 20
(b) AL = 0.5, At = 0.1, n = 50
(c) AL = 0.5, At = 0.01, n = 20
(d) AL = 0.1, At = 0.05, n = 50
11
1068 Pressure depends on distance as, ( boldsymbol{P}= ) ( frac{boldsymbol{alpha}}{boldsymbol{beta}} exp left(-frac{boldsymbol{alpha} boldsymbol{z}}{boldsymbol{k} boldsymbol{theta}}right), ) where ( boldsymbol{alpha}, boldsymbol{beta} ) are
constants, ( z ) is distance, ( k ) is Boltzman’s
constant and ( theta ) is temperature. The
dimensions of ( beta ) are
( mathbf{A} cdotleft[M^{0} L^{0} T^{0}right] )
B ( cdotleft[M^{-1} L^{-1} T-1right] )
( mathbf{c} cdotleft[M^{0} L^{2} T^{0}right] )
D cdot ( left[M^{-1} L^{1} T^{2}right] )
11
1069 While measuring the acceleration due to gravity by a simple pendulum, a
student makes a positive error of ( 1 % ) in the length of the pendulum and a negative error of ( 3 % ) in the value of time
period. His percentage error in the
measurement of ( g ) by the relation ( g= )
( 4 pi^{2}left(l / T^{2}right) ) will be
A . ( 2 % )
в. ( 4 % )
c. ( 7 % )
D. ( 10 % )
11
1070 The radius of proton is ( 0.6 times 10^{-15} m )
What is the order of magnitude of it volume?
A ( cdot 10^{-47} m^{3} )
B . ( 10^{-44} m^{3} )
D. ( 10^{-46} m^{3} )
11
1071 If ( L, C ) and ( R ) denote the inductance, capacitance and resistance
respectively, the dimensional formula
for ( C^{2} ) LR is :
( mathbf{A} cdotleft[M L^{-2} T^{-1} I^{0}right] )
B cdot ( left[M^{0} L^{0} T^{3} I^{0}right] )
( mathbf{c} cdotleft[M^{-1} L^{-2} T^{6} I^{2}right] )
D ( cdotleft[M^{0} L^{0} T^{2} I^{0}right] )
11
1072 The velocity of a particle is given as
( boldsymbol{v}=boldsymbol{a}+boldsymbol{b} boldsymbol{t}+boldsymbol{c} boldsymbol{t}^{2} ). the velocity is
measured in ( mathrm{ms}^{-1} ), then units of a and
( c ) are
( mathbf{A} cdot m s^{-1} ) and ( m s^{-3} )
B. ( m s^{-2} ) and ( m s )
( mathbf{c} cdot m^{2} s ) and ( m s^{2} )
D. ( m s ) and ( m s^{-1} )
11
1073 OU
ities along with the precision of
12. Measure of two quantities along with the pas
respective measuring instrument is
A = 2.5 ms- + 0.5 ms-1, B = 0.10 s + 0.01 s. The value of
AB will be
(a) (0.25 +0.08) m (b) (0.25 +0.5) m
(c) (0.25 + 0.05) m (d) (0.25 +0.135) m
13 You monour tun
10
mo
11
1074 The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If
the relative errors in measuring the mass and length are respectively ( 1.5 % ) and ( 1 % ), the maximum error in
determining the density is?
A . ( 2.5 % )
в. ( 3.5 % )
c. ( 4.5 % )
D. ( 6 % )
11
1075 WIWI HUI
.
15. A body travels uniformly a distance of (13.8 +0.2) m in a
time (4.0 +0.3) s. Calculate its velocity with error limits.
What is the percentage error in velocity?
11
1076 The number of significant figures in
0.00386 is :
A. 5
B. 3
( c cdot 6 )
( D )
11
1077 A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation(T) of the liquid drop depends on radius ( (r) ) of the drop, density ( (rho) ) and surface tension(s) of the liquid. Which among the following will be a possible expression for T(where k is a dimensionless constant)?
A ( cdot k sqrt{frac{rho r}{s}} )
B. ( k sqrt{frac{rho^{2} r}{s}} )
( ^{mathrm{c}} cdot sqrt[k]{frac{rho r^{3}}{s}} )
D. ( k sqrt{frac{rho r^{3}}{s^{2}}} )
11
1078 Mean free time of electrons are
expressed in picosecond( (boldsymbol{p s}) . ) 1ps ( =? )
( mathbf{A} cdot 10^{-12} s )
B ( cdot 10^{-9} s )
( mathbf{c} cdot 10^{-3} s )
D. None of these
11
1079 The diameter of a wire as measured by
screw gauge was found to be
2.620,2.625,2.628 and ( 2.626 mathrm{cm} )
Calculate fractional error.
11
1080 The mass of an oxygen atom is 1600 u. Find its order of magnitude in ( mathrm{kg} ) 11
1081 Three measurements 7.1J, 7.2J and 6.7
are made as experiment and added the result with correct number of
significant figures is
A . 7.1
B . 7.06
c. 7.0
D. 7]
11
1082 The unit of molar susceptibility is
A ( cdot k g^{-1} m^{3} )
в. ( k g m^{3} )
( c cdot m^{3} )
D. Unit less
11
1083 The mass of a ball is ( 1.76 k g . ) The mass
of 25 such balls is
A. ( 440.00 mathrm{kg} )
в. ( 44.40 k g )
c. ( 44.0 k g )
D. 44.00kg
11
1084 Find the order of magnitude of 38500 ( mathbf{k g} ) 11
1085 Which of the following pairs have same dimensions.
a) Torque and work
b) Angular momentum and work
c) Energy and Youngs modulus
d) Light year and wavelength
( A cdot ) a and ( b ) are correct
B. b and c are correct
c. c and d are correct
D. d and a are correct
11
1086 A Standard unit does not change with respect to space and time.
A . True
B. False
11
1087 Write the S.I unit of three fundamental
quantities.
11
1088 Give reasons as to why equal masses of different substances have different
volumes.
A. because they have different shapes
B. because they have different densities
c. because they have the same densities
D. none of these
11
1089 Which of the following physical quantities has no unit?
A. Relative density
c. Pressure
D. Thrust
11
1090 The least count of a stop watch is 0.2 s.
The time of 20 oscillations of a
pendulum is measured to be 25 s. The percentage error in the measurement of
time will be:
A . ( 16 % )
в. 1.8 %
c. ( 0.8 % )
D. 0. %
11
1091 If voltage ( V=(100 pm 5) vee ) and current ( I= )
( (10 pm 0.2) A, ) the percentage error in resistance R is
A . ( 5.2 % )
B . 25%
c. ( 7 % )
D. 10%
11
1092 Write the dimensional formula of
pressure.
11
1093 The physical quantity having the same unit in all the systems of unit is :
A. length
B. mass
c. time
D. foot
11
1094 Of the following quantities which one has the dimensions different from the
remaining three?
A. Energy density
B. Force per unit area
c. Product of charge per unit volume and voltage
D. Angular momentum per unit mass
11
1095 One second is defined to be equal to:
A. 1650763.73 periods of krypton clock
B. 652189.63 periods of krypton clock
C. 1650755.73 periods of cesium clock
D. 9,19,26,31,770 periods of cesium clock
11
1096 1. Why do we have different units for the same physical
quantity?
11
1097 Calculate the number of light years in a
petametre. (where ( left.1 text { peta }=10^{15} mright) 1 )
11
1098 The dimensions of ( frac{v^{2}}{mu g} ) where ( mu= )
coefficient of friction, ( boldsymbol{v}= ) the velocity
( g= ) acceleration due to gravity is same
as that of
( ^{A} cdot frac{F}{B q} )
в. ( mu F )
c. ( frac{F}{m} )
D. None
11
1099 21. The dimensional formula for Planck’s constant (a) is 11
1100 ‘The parallax angle in radians is: ( boldsymbol{theta}= ) ( left(1+frac{54}{60}right) times frac{pi}{180}=0.03316 mathrm{rad} )
Hence, the distance between moon and earth:
A. ( frac{text { Diameter of Earth }}{theta} )
в. ( frac{1.276 times 10^{7} m}{0.03316} )
c. ( 3.84 times 10^{8} m )
D. nnone of these
11
1101 Calculate the area enclosed by a circle
of diameter ( 1.12 m ) to the correct
number of significant figures.
11
1102 Add ( 3.8 times 10^{-6} ) to ( 4.2 times 10^{-5} ) with due
regard to significant figures.
begin{tabular}{ll}
A. ( 4.6 times 10^{-5} ) & 5 \
hline
end{tabular}
в. ( 4.6 times 10^{-6} )
c. ( 5.6 times 10^{-6} )
D. ( 6.6 times 10^{-5} )
11
1103 The length of a strip measured with a
meter rod is ( 10.0 mathrm{cm} ) its width measured
with a vernier caliper is ( 1.00 mathrm{cm} . ) The least count of the meter rod is ( 0.1 mathrm{cm} ) and that of vernier caliper caliper 0.01 ( mathrm{cm} ) water will be error in its area?
( mathbf{A} cdot pm 13 % )
B. ( pm 7 % )
( c . pm 4 % )
D. ( pm 2 % )
11
1104 In the expression ( y=a sin (omega t+theta), y )
is displacement and ( t ) is the time. Write
the dimensions of ( omega )
( mathbf{A} cdotleft[M^{0} L T^{0}right] )
В ( cdotleft[M^{0} L^{0} T^{0}right] )
C . ( left[M^{0} L^{0} T^{-1}right. )
( mathbf{D} cdotleft[M^{1} L^{0} T^{0}right] )
11
1105 The dimension of mass is zero in which
of the following physical quantities?
A. Gravitational potential
B. Latent heat
c. specific heat capcity
D. All of the above
11
1106 Which of the following statements below should be followed while using the symbol for a unit of a physical quantity? This question has multiple correct options
A. The symbol named after a scientist should begin with a capital letter
B. They can take plural forms.
c. They can be written in full
D. They should be written only in the agreed symbols while using symbols.
11
1107 A wire has a mass ( 0.3 pm 0.003 mathrm{g} ), radius
( mathbf{0 . 5} pm mathbf{0 . 0 0 5} boldsymbol{m m} ) and length ( boldsymbol{6} pm )
( 0.06 mathrm{cm} . ) The maximum percentage
error in the measurment of its density is
A . 1
B. 2
( c .3 )
D. 4
11
1108 The Vanderwaal’s equation for a gas is ( left(p+frac{a}{V^{2}}right)(V-b)=n R T, ) where ( P, v )
R, ( T ) and ( n ) represent the pressure, volume, universal gas constant, absolute temperature, and number of moles of a gas respectively and ‘a’ and ‘b’ are constants. The ratio ( frac{b}{a} ) will have the following dimensional formula:
( mathbf{A} cdot M^{-1} L^{-2} T^{2} )
В. ( M^{1} L^{-1} T^{-1} )
c. ( M L^{2} T^{2} )
D. ( M L T^{-2} )
11
1109 What is parallax? Explain. 11
1110 Which of the statements are correct?
This question has multiple correct options
A. Unit of work is ( mathrm{kgm}^{2} mathrm{s}^{-2} )
B. Unit of force is ( k g m s^{-2} )
C. Unit of work is ( k g m s^{-2} )
D. Unit of force is ( k g m^{2} s^{-2} )
11
1111 The sun’s angular diameter is
measured to be ( 1920^{prime prime} . ) The distance of
the sun from the earth is ( 1.496 times )
( 10^{11} ) m. What is the diameter of the sun?
A ( cdot 1 times 10^{9} m )
В. ( 1.39 times 10^{9} m )
c. ( 13.9 times 10^{9} mathrm{m} )
D. ( 139 times 10^{9} m )
11
1112 Arrange the following physical quantities in the increasing order of their magnitudes
I. 1 dyne
II. ( 1 N )
III. ( 3 k g m s^{-2} )
IV. ( 10^{7} g c m s^{-2} )
( mathbf{A} cdot |, 1, ) ॥I ( , ) IV
B. IV, ।, ॥ᅵ, ॥
c. ॥, ॥ा, ।, IV
D. I, II, III, IV
11
1113 The prefix used to represent ( 10^{-2} ) is called
A . Mill
B. Centi
c. кilo
D. Deci
11
1114 In Searle’s exp to find Young’s modulus, the diameter of wire is measured as ( mathrm{D}= ) ( 0.05 mathrm{cm}, ) length of wire is ( mathrm{L}=125 mathrm{cm}, ) and when a weight, ( m=20.0 mathrm{kg} ) is put, extension in wire was found to be 0.100
cm. Find maximum permissible error in young’s modulus (Y).
A . 43 %
в. 6.3%
c. ( 0.63 % )
D. 630%
11
1115 Mention two advantages of the metric
system.
11
1116 Percentage errors in the measurement of mass and speed are ( 2 % ) and ( 3 % ) respectively. The error in the estimation
of kinetic energy obtained by measuring mass and speed will be:
A. 8%
B. २%
c. 12%
D. 10%
11
1117 Dimensional analysis of the equation
( (V e l o c i t y)^{x}= )
( (text {Pressuredifference})^{frac{3}{2}} cdot(text { density })^{frac{-3}{2}} )
gives the value of ( x ) as:
( A )
B. 2
( c cdot 3 )
( D cdot-3 )
11
1118 The equation of .a wave, travelling with
amplitude ( A, ) linear ( u, ) angular velocity ( omega ) is given by
( boldsymbol{y}=boldsymbol{A} sin boldsymbol{omega}left(frac{boldsymbol{x}}{boldsymbol{v}}-boldsymbol{k}right) )
The dimensions of ‘k’ are
A . ( [T] )
B ( cdotleft[T^{-1}right] )
( mathbf{c} cdotleft[T^{-2}right] )
D・ ( left[T^{2}right] )
11
1119 Sl unit of momentum is
A. dyne ( cdot )sec
в. ( g cdot mathrm{cms}^{-1} )
c. ( N s )
( mathbf{D} cdot g m cdot s )
11
1120 Assertion
The number 1.202 has four significant
figures and the number 0.0024 has two significant figures.
Reason
All the non zero digits are significant.
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
1121 Illustration 1.3 Convert gravitational constant (G) from CGS
to MKS system.
11
1122 22. If the percentage errors
the percentage errors of A, B, and C are a, b, and c,
respectively, then the total percentage error in the product
ABC is
a. abc
b. a + b + c
-+-+-
a b
d. ab + bc + ca
c
11
1123 State whether the given statement is True or False :

The force on a mass m due to gravity is
( mathrm{mg} )
A. True
B. False

11
1124 The sum of the numbers 436.32,227.2 and 0.301 in appropriate significant figures is then
A . 663.821
B. 664
c. 663.8
D. 663.82
11
1125 Round off 2.0082 to four significant figures.
A . 2.008
B. 2.0082
c. 2.009
( D )
11
1126 ( frac{boldsymbol{alpha}}{boldsymbol{t}^{2}}=boldsymbol{F} boldsymbol{v}+frac{boldsymbol{beta}}{boldsymbol{x}^{2}} )
Find the dimensional formula for ( [boldsymbol{alpha}] )
and ( [beta] ) using the given equation
(here ( t= ) time, ( F= ) force, ( v= ) velocity, ( x= ) distance)
11
1127 Systematic error occurred due to poor
calibration of instrument that can be
corrected by
A. taking several readings
B. replacing instruments
c. taking mean of values
D. taking median of values
11
1128 The Sl unit of ( frac{1}{2 pi sqrt{L C}} ) is equivalent to
that of :
A. time period
B. frequency
c. wavelength
D. wave number
11
1129 The position of a particle at time ( t ) is given by the relation ( boldsymbol{x}=frac{boldsymbol{v}_{0}}{boldsymbol{alpha}}left(mathbf{1}-boldsymbol{e}^{-boldsymbol{alpha} t}right) )
The dimensional formula for ( boldsymbol{alpha}^{2} boldsymbol{v}_{0}^{3} ) will
be :
11
1130 Which of the following sets cannot enter into the list of fundamental quantities in any system of units?
A. length, mass and velocity
B. length, time and velocity
c. mass, time and velocity
D. length, time and mass
11
1131 Assertion
Absolute error may be negative or
positive.
Reason
Absolute error is the difference between
the real value and the measured value
of a physical quantity
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
1132 A famous relation in physics relates
‘moving mass’ ( mathrm{m} ) to the ‘rest mass’ ( boldsymbol{m}_{mathbf{0}} ) of a particle in terms of its speed v and the speed of light, c. (This relation first arose asa consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He
writes:
( boldsymbol{m}=frac{boldsymbol{m}_{o}}{left(mathbf{1}-boldsymbol{v}^{2}right)^{1 / 2}} )
Guess where to put the missing c.
11
1133 Which of the following is used as ( mathrm{S} ) I prefix:
This question has multiple correct options
A . Mega
B. Hecto
c. Tera
D. Mara
11
1134 In resonance tube experiment, the velocity of sound is given by ( boldsymbol{v}= )
( 2 f_{0}left(l_{1}-l_{1}right) . ) We found ( l_{1}=25.0 c m ) and
( l_{2}=75.0 c m . ) If there is no error in
frequency, what will be the maximum
permissible error in the speed of sound? ( left(text {Take} f_{0}=mathbf{3 2 5 H z}right) )
11
1135 Which of the following statements are true for density?
A. It is a physical property of matter
B. It is a scalar quantity
c. It is the mass per unit volume of a substance
D. All of the above
11
1136 Write the number of significant digits
in 100.1
11
1137 Illustration 1.19 Repeated observations in an experiment
gave the values 1.29, 1.33, 1.34, 1.35, 1.32, 1.36, 1.30, and
1.33. Calculate the mean value, absolute error, relative error,
and percentage error.
11
1138 1 parsec = metres 11
1139 Assertion
A piece of ice, with a stone frozen inside
it, floats on water in a beaker. When the
ice melts, the level of water in the
beaker decreases.
Reason
Density of stone is more than of water
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
1140 Name any two units of length which are bigger than the metre. Write the
relation
between each of those units and the
metre.
11
1141 What are the dimensions of ( boldsymbol{K}=frac{mathbf{1}}{mathbf{4} boldsymbol{pi} boldsymbol{epsilon}_{0}} ? )
(Given, N is the unit of force, with
dimensions ( M L T^{-2} ) )
A ( cdot C^{2} N^{-1} M^{-2} )
в. ( N M^{2} C^{-2} )
c. ( N M^{2} C^{2} )
D. Unitless
11
1142 Quantity ( X ) has a fractional uncertainty
of ( x . ) Quantity ( Y ) has a fractional uncertainty of ( y ) What is the fractional uncertainty in ( frac{boldsymbol{X}}{boldsymbol{Y}^{2}} )
( mathbf{A} cdot x+y )
в. ( x-y )
c. ( x+2 y )
D. ( x-2 y )
11
1143 Illustration 1.20 A physical parameter a can be determined
by measuring the parameters b, c, d, and e using the relation a
= bºld’e”. If the maximum errors in the measurement of b,c,
d, and e are b,%,c,%, d,%, and e,%, then find the maximum
error in the value of a determined by the experiment.
11
1144 The initial and final temperatures of a
liquid are measured to be ( 67.7+0.2^{0} C )
and ( 76.3+0.3^{0} C )
Calculate the rise in temperature with error limits.
A ( cdot 8.6 pm 0.5^{circ} mathrm{C} )
B ( .9 pm 0.5^{0} C )
( mathbf{c} cdot 16 pm 0.5^{0} C )
D. ( 2.6 pm 0.5^{circ} mathrm{C} )
11
1145 The value due regard to significant figure ( 4.0 times 10^{-4}-2.5 times 10^{-6} )
A ( cdot 4.0 times 10^{-4} )
B. ( 3.975 times 10^{-4} )
c. ( 3.9 times 10^{-4} )
D. none of the above
11
1146 Illustration 1.27 The length and breadth of a field are
measured as: I=(1202)m and b=(100+5) m, respectively.
What is the area of the field?
11
1147 The proper value of significant figures in ( 38.0+0.0035+0.00003 ) is:
A . 38
B. 38.0035
c. 38.00353
D. 38.0
11
1148 A boy wants to buy new shoes. To find
out his correct shoe size the
of his feet should
be measured
A. Length
B. Thickness
c. Area
D. volume
11
1149 c. 13%
d. 20%
04. Using mass (M), length (L), time (T), and electric
current (A) as fundamental quantities, the dimensions of
permittivity will be
a. [MLT-‘A-‘) b. [M LT-2 A-21
c. M-‘L-314 A21 d. [
ML-21-2 A1
11
1150 1. Planck’s constant has dimensions –
(IT JEE, 1985)
11
1151 Universal gravitational constant is given by ( 6.67 times 10^{-11} N m^{2} k g^{-2} . ) Then
the no. of significant figures in it is:
A . 14
B. 2
( c cdot 3 )
D. 11
11
1152 1: Method of dimensions cannot be used
for deriving formulae containing trigonometrical ratios.
2: Trigonometrical ratios are dimensionless.
A. 1 and 2 are correct and 2 is correct explanation of
B. 1 and 2 are correct and 2 is not correct explanation of
( c .1 ) is true and 2 is false
D. 1 is false and 2 is true
11
1153 Given that force ( F ) is given by, ( boldsymbol{F}= )
( boldsymbol{P t}^{-1}+boldsymbol{Q} boldsymbol{t}, ) where ( t ) is the time. The unit
of ( P ) is same as that of
A. velocity
B. acceleration
c. displacement
D. momentum
11
1154 The correct way to represent ( 10^{9} W ) is
( mathbf{A} cdot 1 G W )
в. ( 1 M W )
( mathbf{c} cdot 1 T W )
D. none of these
11
1155 A rectangular block ( 5 mathrm{m} times 4 mathrm{m} times 2 mathrm{m} ) lies
on a table with its largest surface in contact with the table. The work done to
keep it so that the block rests on the smallest surface is, if its density is 600 ( mathbf{k} boldsymbol{m}^{-mathbf{3}} )
A . 352800 J
B. zero
c. ( 376000 mathrm{J} )
D. ( 24,0000 mathrm{J} )
11
1156 What is the ratio of CGS to MKS unit of
acceleration?
A ( cdot frac{m}{c m} )
в. ( frac{m}{s} )
c. ( frac{c m}{s} )
D. ( frac{c m}{m} )
11
1157 The prefixes ( n a n o(n), m i c r o(mu) ) and pico ( (p) ) are often used with units.
Which row shows their correct values?
A ( cdot n=10^{-6}, mu=10^{-9}, p=10^{-12} )
B . ( n=10^{-6}, mu=10^{-12}, p=10^{-9} )
C ( . n=10^{-9}, mu=10^{-6}, p=10^{-12} )
D . ( n=10^{-12}, mu=10^{-9}, p=10^{-6} )
11
1158 If the values of force and length are increased four times, then the unit of
energy will be increase by:
A. 4 times
B. 2 times
c. 8 times
D. 16 times
11
1159 If unit of mass, length and time are
tripled, then unit of energy becomes:
( mathbf{A} cdot mathbf{3} )
B. ( frac{1}{3} )
c. 9
D.
11
1160 The average kinetic energy ( E ) of a gas
molecule is given by the equation ( boldsymbol{E}= )
( frac{3}{2} k T )
where ( T ) is the absolute (kelvin
temperature)

What are the SI base units if ( k ) ?
A ( cdot k g^{-1} m^{-1} s^{2} K )
B. ( k g^{-1} m^{-2} s^{2} K )
c. ( k g m s^{-2} K^{-1} )
D. ( operatorname{kgm}^{2} s^{-2} K^{-1} )

11
1161 If the length of a simple pendulum is recorded as ( (90.00 pm 0.02) mathrm{cm} ) and period as ( (1.90 pm 0.02) mathrm{s}, ) the
percentage of error in the measurement of acceleration due to
gravity is :
A . 4.2
B . 2.
c. 1.5
D. 2.8
11
1162 Assertion
The Sl unit of volume is ( m^{3} )
Reason
Volume is a derived quantity of length.
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
1163 If the velocity of light ( C, ) the universal
gravitational constant ( G, ) and Planck’s
constant ( h ) are chosen as fundamental
units, the dimension of mass in this
system are
A ( cdot h^{1 / 2} C^{1 / 2} G^{-1 / 2} )
( mathbf{B} cdot h^{-1} C^{-1} G )
( c cdot h C G^{-1} )
D. ( h C G )
11
1164 Velocity of light in centimeter per nano second is 11
1165 Illustration 1.7 Convert 54 km h-‘ into ms. 11
1166 A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading:
58.5 degree, Vernier scale reading : 9 divisions. Given that 1 division on main
scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and
match with 29 divisions of the main
scale. The angle of the prism from the above data:
A . 58.59 degree
B. 58.77 degree
c. 58.65 degree
D. 59 degree
11
1167 Which of the following equation is dimensionally correct?
A. Pressure = Energy per unit area
B. Pressure = Energy per unit volume
c. Pressure = Force per unit volume
D. Pressure = Momentum per unit volume per unit time
11
1168 Can a physical quantity have units but still be dimensionless? 11
1169 C. Cum
d. I/CUTEN
51. The moment of inertia of a body rotating about a given axis is
12.0kg m’in the SI system. What is the value of the moment
of inertia in a system of units in which the unit of length is
5 cm and the unit of mass is 10 g?
a. 2.4 x 103
b. 6.0 x103
c. 5.4 x105
d. 4.8×105
11
1170 The S.I. unit of magnetic pole strength is
A ( . A . m^{2} )
B. ( A . m^{-1} )
c. A.m
D. ( A / m^{2} )
11
1171 ( mathbf{1}^{o} boldsymbol{A} ) is
A. ( 10 n m )
B. ( 0.1 n m )
c. 100 n ( m )
D. ( 1 n m )
11
1172 The number of significant figures in
0.06900 is the
A. 5
B. 4
( c cdot 2 )
( D )
11
1173 The dimensions of universal gas
constant are
( mathbf{A} cdotleft[L^{2} M^{1} T^{-2} K^{-1}right] )
B ( cdotleft[L^{1} M^{2} T^{-2} K^{-1}right] )
c. ( left[L^{1} M^{1} T^{-2} K^{-1}right] )
D ( cdotleft[L^{2} M^{2} T^{-2} K^{-1}right] )
11
1174 The refractive index ( (mu) ) of glass is found to have the values
1.49,1.50,1.52,1.54 and 1.48
Calculate absolute error is each
measurement
A ( cdot Delta n_{5}=1.51-1.48=+0.03 )
B . ( Delta n_{4}=1.51-1.54=-0.03 )
C ( . Delta n_{3}=1.51-1.52=-0.01 )
D. All of these
11
1175 Express 0.006006 into scientific
notation in three significant digits:
A ( cdot 6.01 times 10^{-3} )
B . ( 6.0006 times 10^{-3} )
c. ( 6.00 times 10^{-3} )
D. ( 6.0 times 10^{-3} )
11
1176 Femto is ( =10^{-x}, ) then ( x=? ) 11
1177 A watch shows time as 3: 25 when seen
through a mirror, time appeared will be
then
( A cdot 8: 35 )
B. 9: 35
( c cdot 7: 35 )
D. 8: 25
11
1178 In the experiment of verification of Ohms law the error in the current measurement
is ( 1 % ), while that in the voltage
measurement is ( 2 % ). The error in the
resistance has a maximum value of
A . 1%
B. 2%
c. 3%
D. none of these
11
1179 With a highly advanced precision instrument:
A. percentage error can be reduced
B. totally accurate value can be measured
c. true value can be found out
D. all the above
11
1180 The length, breadth and thickness of a rectangular sheet of metal are ( 4.234 mathrm{m} ) ( 1.005 mathrm{m}, ) and ( 2.01 mathrm{cm} ) respectively. Give
the area and volume of the sheet to
correct significant figures.
11
1181 Measure of two quantities along with the precision of respective measuring instrument is
( boldsymbol{A}=mathbf{2 . 5 m s}^{-1} pm mathbf{0 . 5 m s}^{-1}, boldsymbol{B}=mathbf{0 . 1 0 s} pm )
( mathbf{0 . 0 1 s} )
The value of ( A B ) will be
( mathbf{A} cdot(0.25 pm 0.08) m )
в. ( (0.25 pm 0.8) m )
c. ( (0.25 pm 0.05) m )
D. ( (0.25 pm 0.135) m )
11
1182 Sl unit of Magnetic flux is weber and its CGS unit is maxwell. Then ( 1 mathrm{Wb}= )
A ( cdot 10^{6} ) maxwel
B . ( 10^{7} ) maxwell
c. ( 10^{8} ) maxwell
D. ( 10^{9} ) maxwell
11
1183 39. The quantities A and B are related by the relation A/B =
m, where m is the linear mass density and A is the force,
the dimensions of B will be
a. Same as that of pressure
b. Same as that of work
c. That of momentum
d. Same as that of latent heat
11
1184 If energy (E), force (F) and linear
momentum (P) are fundamental
quantities, then match the following
and give correct answer.
( mathbf{A} ) B
Physical quantity Dimensional formula
Mass ( E^{0} F^{-1} p^{1} )
a)
d)
b) Length
e) ( E^{-1} F^{0} p^{2} )
Time ( E^{1} F^{-1} p^{0} )
c)
f) ( r ) 1 an
( A cdot a-d, b-e, c-f )
B. a-f, b-e, c-d
( mathbf{C} cdot a-e, b-f, c-d )
D. a-e, b-d, c-f
11
1185 The dimensions of ( frac{a}{b} ) in the equation ( P=frac{a-t^{2}}{b x}, ) where ( P ) is pressure, ( x ) is
distance and ( t ) is time, are
A ( cdotleft[M^{2} L T^{-3}right] )
в. ( left[M T^{-2}right] )
( mathbf{c} cdotleft[L T^{-3}right] )
( mathbf{D} cdotleft[M L^{3} T^{-1}right] )
11
1186 9. The diameter of a sphere is 3.34 m. Calculate its volume
with due regard to significant figures.
o
a
11
1187 Boiling point of water on the Fahrenheit scale is
( mathbf{A} cdot 100^{circ} mathrm{F} )
В. ( 112^{circ} mathrm{F} )
c. ( 212^{circ} ) F
D. 32 ( ^{circ} )
11
1188 A bottle can hold ( 100 g ) of water at ( 40^{circ} mathrm{C} )
What mass of sea water (Density ( = ) ( left.1030 k g / m^{2}right) ) can it hold?
11
1189 Which of the following is a unit of distance?
A. second
B. Candela
c. мо।
D. Light year
11
1190 6. Which of the following is not the unit of energy?
(a) Calorie
(b) Joule
(c) Electron volt (d) Watt
11
1191 Assertion
Statement I : A physical quantity can be regarded as a vector, if magnitude as well as direction is associated with it.
Reason

Statement II : A physical quantity can be regarded as a scalar quantity, if it is associated with magnitude only.
A. Statement-I is false, Statement-II is true
B. Statement-I is true, Statement-II is false
c. statement-l is true, statement-ll is true ; statement-I is NOT a correct explanation for Statement-
D. Statement-l is true, Statement-II is true ; Statement-I is correct explanation for Statement-

11
1192 The wavelength of monochromatic light is ( 6000 A^{0} . ) Write this value in ( n m ) 11
1193 5. Which of the following pairs has/have the same
dimensions?
a. Reynold number and coefficient of friction
b. Curie and frequency of light wave
c. Latent heat and gravitational potential
d. Planck’s constant and torque (IIT JEE, 1995)
11
1194 The accuracy of measurement also lies
in the way the result is expressed. The number of digits to which a value is to
be expressed is one digit more than
number of sure numbers. Rules do exist
to deal with number of digits after an
operation is carried out on the given values. The error can be minimised by
many trials and using the correct methods and instruments.
If the length and breadth are measured as 4.234 and ( 1.05 mathrm{m}, ) the area of the
rectangle is
A ( .4 .4457 m^{2} )
B . ( 4.45 mathrm{m}^{2} )
c. ( 4.446 m^{2} )
D. ( 0.4446 m^{2} )
11
1195 Identify which of the following
statements is true?
A. Displacement is a scalar and distance is a vector
B. Displacement is a vector and distance is scalar.
c. Both displacement and distance are vectors.
D. Neither displacement nor distance the vectors
E. Displacement and distance are slangs equal
11
1196 One ohm is equal to
( mathbf{A} cdot 10^{6} M Omega )
B ( cdot 10^{9} M Omega )
( mathbf{c} cdot 10^{-6} M Omega )
D. none of these
11
1197 Write the number of significant figures
for 1.0076
11
1198 Name one unit of time bigger than a
second.
A. plank time
B. zeptosecond
c. picosecond
D. kilosecond
11
1199 Fill in the Blanks
Angular displacement is a vector quantity for (very small/even large)
11
1200 The dimensions of ( epsilon_{0} mu_{0} )
( mathbf{A} cdotleft[L T^{-1}right] )
B . ( left[L T^{-2}right] )
c. ( left[L^{2} T^{-2}right] )
( mathbf{D} cdotleft[L^{-2} T^{-2}right] )
11
1201 Write the order of magnitude of mass of an electron ( 9.1 times 10^{-31} mathrm{kg} ) 11
1202 The shaded portion on a 24 hour clock given below tells the sleeping time of a sloth’ (a bear). Find the time for which
the sloth is asleep. Find the time for which the sloth is awake. If it sleep at 6 h 15 min then when does the sloth
awake.
11
1203 Length, breadth and thickness of a rectangular slab are ( 4.234 mathrm{m}, 1.005 mathrm{m} ) and ( 2.01 mathrm{m} ) respectively. Find volume of the slab to correct significant figures.
( mathbf{A} cdot 8.55 m^{3} )
в. ( 8.552 m^{3} )
c. ( 8.6 m^{3} )
D. None of the above
11
1204 Statement -1: Kinetic energy can be divided by volume and
Statement -2: Dimensions of kinetic
energy and volumeare different
A. Statement- -1 is True Statement-2 is True
Statement-2 is a correct explanation for Statement-
B. Statement- – – is True Statement-2 is True:
Statement-2 is NOT a correct explanation for Statement-1
c. statement – – is True Statement – – 2 is False.
D. Statement-1 is False Statement- -2 is True
11
1205 Illustration 1.24 The initial and final temperatures of water as
recorded by an observer are (40.6+0.2)°C and (78.9+0.3)°C.
Calculate the rise in temperature with proper error limits.
11
1206 The interval of time that elapses between two consecutive passages of a fixed star (other than the sun) across the meridian is called
A. mean solar day
B. mean sidereal day
C. mean solar year
D. mean sidereal year
11
1207 Temperature is measured in degree 11
1208 Pressure is dimensionally:
This question has multiple correct options
A. Force per unit area
B. Energy per unit volume
C. Momentum per unit area per second
D. Momentum per unit volume
11
1209 Simplify and round to the appropriate number of significant digits
( (a) 16.235 times 0.217 times 5 )
(b) ( 0.00435 times 4.6 )
11
1210 Two students ( P ) and ( Q ) perform an experiment to verify Ohm’s law for a conductor with resistance R. They use a current source and a voltmeter with
least counts of ( 0.1 mathrm{mA} ) and ( 0.1 mathrm{mV} )
respectively. The plots of the variation of voltage drop(V) across R with current(i)
for both are shown. the statement which
is most likely to be correct is?
A. P has only random error(s)
B. Q has only systematic error(s)
c. ( Q ) has both random and systematic errors
D. P has both random and systematic errors
11
1211 The velocity ( v ) of a particle at time ( t ) is
given by ( v=a t+frac{b}{t+c}, ) where ( a, b ) and ( c )
are constants.The dimensions of
( a, b ) and ( c ) are respectively:
( mathbf{A} cdot mathrm{LT}^{-2}, mathrm{L} ) and ( mathrm{T} )
B. ( L^{2}, ) T and ( L T^{2} )
c. ( L^{2} ), LT and ( L )
D. L, LT and ( T^{2} )
11
1212 Q Type your question ( sqrt{07} )
What is and
( mathbf{A} cdot(A) )
( -b-t-3 )
( (B) )
( -c-s-4 )
( (C) )
( -a-q-1 )
( (D) )
( -e-r-5 )
( (E) )
( -d-p-2 )
( mathbf{B} cdot(A) )
( -c-s-3 )
( (B) )
( -b-s-4 )
( (C) )
( -a-t-1 )
( (D) )
( -e-r-5 )
( (E) )
( -d-p-2 )
( mathbf{C} cdot(A) )
( -d-p-3 )
( (B) )
( -e-r-4 )
( (C) )
( -a-q-1 )
( (D)-c-s-5 )
( (E)-b-t-2 )
D. None of these
11
1213 Which of the following is not a unit of time?
A. Mean solar day
B. Lunar Month
C. Calendar year
D. Light year
11
1214 If power (P), surface tension (S) and Planck’s constant (h) are arranged so that the dimensions of time in their
dimensional formulae are in ascending order, then which of the following is correct then?
( A cdot P, S, h )
B. P, h, S
( c cdot s, P, h )
D. s, h, P.
11
1215

0
as d
un 15u00.
10. Solve with due regard to significant figures:
5.42 x 0.6753
0.085
11
1216 Assertion
Light year and wavelength have same
dimensional formula.
Reason
Both have the dimensions of time
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
1217 ( sqrt{mu_{0} epsilon_{0}} ) has the dimensions
( mathbf{A} cdotleft[M^{0} L T^{-1}right] )
В . ( left[M^{0} L^{-1} Tright] )
( mathbf{c} cdotleft[M^{2} L^{3} T^{-1}right] )
D cdot ( left[M^{-1} L^{3} T^{-2}right] )
11

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