Mechanical Properties Of Solids Questions

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Mechanical Properties Of Solids Questions

List of mechanical properties of solids Questions

Question NoQuestionsClass
1A wire of radius ( r, ) Youngs modulus ( Y ) and length ( l ) is hung from a fixed point and supports a heavy metal cylinder of volume ( V ) at its lower end. The change
in length of wire when cylinder is immersed in a liquid of density ( rho ) is in fact
A ( cdot ) decreases by ( frac{V l rho g}{Y pi r^{2}} )
B. increases by ( frac{V r rho g}{Y pi l^{2}} )
c. decreases by ( frac{V rho g}{Y pi r} )
D. increases by ( frac{V rho g}{pi r l} )
11
2A material has poisson’s ratio of ( 0.5 . ) If a uniform rod suffers a longitudinal strain of ( 2 times 10^{-3} ) the percentage
increase in its volume is :
A . २%
в. 0.5%
c. ( 4 % )
D. 0%
11
3Substances that break just after elastic
limit is reached are known as
A. brittle substances
B. breakable substances
c. ductile substances
D. elastic substances
11
4The following substances which possess rigidity modulus
A. Only Solids
B. Only liquids
c. Liquids and Gases
D. solids, Liquids and Gases
11
5The stress at which extension of the
material takes place more quickly as compared to the increase in load is called
A. Elastic point of the material
B. Plastic point of the material
c. Breaking point of the material
D. Yield point of the material
11
6The Poissons ratio of a material is ( 0.4 . ) If
a force is applied to a wire of this material, there is a decrease of the
cross-sectional area by ( 2 % ). The percentage increase in its length is
A . ( 3 % )
в. 2.5%
c. ( 1 % )
D. 0.5%
11
7Two metal wire ‘P’ and ‘Q’ of same length and material are stretched by same
load. Their masses are in the ratio ( boldsymbol{m}_{1}: )
( m_{2} . ) The ratio of elongations of wire ‘P’ to
that of ‘Q’ is
A ( cdot m_{1}^{2}: m_{2}^{2} )
в. ( m_{2}^{2}: m_{2}^{1} )
( mathrm{c} cdot m_{2}: m_{1} )
D. ( m_{1}: m_{2} )
11
8If the ratio of diameters, lengths and
Young’s moduli of steel and brass wires
shown in the figure are ( p, q ) and ( r )
respectively. Then the corresponding ratio of increase in their lengths would
be:
A ( frac{3 q}{5 n^{2} r} )
в. ( frac{5 q}{3 p^{2}} )
c. ( frac{3 q}{5 p r} )
D. ( frac{5 q}{p r} )
11
9Which of the following statements is correct regarding Poisson’s ratio?
A. It is the ratio of the longitudinal strain to the lateral strain
B. Its value is independent of the nature of the material
C. It is unitless and dimensionless quantity
D. The practical value of Poisson’s ratio lies between 0 and 1
11
10A cable that can support a load of 1000 N is cut into equal parts. the maximum load that can be supported by the either part is:-
A . ( 1000 mathrm{N} )
B. 2000 N
c. ( 500 mathrm{N} )
D. 250 N
11
11Longitudinal strain can be produced in :
A. glass
B. water
c. honey
D. hydrogen gas
11
12A steel rope has length ( L ), area of cross-
section ( A ), Young’s modulus ( Y ) and density as ( d ). It is pulled on a horizontal
frictionless floor with a constant horizontal force ( F=frac{d A L g}{2} ) applied at one
end. Find the strain at the midpoint.
( mathbf{A} cdot frac{d g L}{2 Y} )
B. ( frac{d g L}{4 Y} )
( mathbf{c} cdot frac{d g L}{6 Y} )
D. ( frac{d g L}{8 Y} )
11
13There are two wires of same material
and same length while the diameter of second wire is two times the diameter
of first wire, then the ratio of extension
produced in the wires by applying same load will be
A . 1: 1
B . 2: 1
c. 1: 2
D. 4: 1
11
14A wire is stretched to double its length.
The strain is :
A. infinity
B.
c. zero
D. 0.5
11
15Two wires of same material and length
but cross-sections in the ratio 1: 2 are
used to suspend the same loads. The extensions in them will be in the ratio
A .1: 2
B . 2: 1
c. 4: 1
D. 1: 4
11
16Two light wires made up of the same material (Young Modulus, Y) have
length ( L ) each and radii ( R ) and ( 2 R ) respectively, They are joined together and suspended from a rigid
support. Now a weight ( W ) attached to
the free end of the joint wire as shown in the figure. Find the elastic potential energy stored in the system due to the
extension of the wire
11
17ILLUSTRATION 33,5 A student performs an experiment to
determine the Young’s modulus of a wire, exactly 2 m long, by
Searle’s method. In a particular reading, the student measures
the extension in the length of the wire to be 0.8 mm with an
uncertainty of +0.05 mm at a load of exactly 1.0 kg. The
student also measures the diameter of the wire to be 0.4 mm
with an uncertainty of +0.01 mm. Take g = 9.8 m/s’ (exact).
The Young’s modulus obtained for the reading is
(a) (2.0 + 0.3)10 N/m2
(b) (2.0 +0.2) x 10 N/m?
(c) (2.0 + 0.1) X 10′ N/m?
(d) (2.0 + 0.05) x 10 N/m²
ed
nat
11
18The length of a rubber cord is ( l_{1} ) metres
when the tension in it is ( 4 N ) and ( l_{2} )
metres when the tension is ( 5 N ). then the
length in meters when the tension is ( mathbf{9} N ) is
A ( cdot 3 l_{2}+4 l_{1} )
B . ( 3 l_{2}+2 l_{1} )
( mathbf{c} cdot 5 l_{2}-4 l_{1} )
D. ( 3 l_{2}-2 l_{1} )
11
19Assertion
(A): Rigidity modulus of a liquid is infinity. Reason (R): For a ductile material yield point and breaking point are separated by larger distance than for brittle materials on the stress-starin curve.
A. Both assertion and reason are true and the reason is correct explanation of the assertion
B. Both assertion and reason are true, but reason is not correct explanation of the assertion
c. Assertion is true, but the reason is false
D. Assertion is false, but the reason is true
11
20Which of the following are close to ideal plastics?
This question has multiple correct options
A. Putty
B. Mudd
c. Rubber band
D. None of the above
11
21Total elongation of the wire.11
22When temperature of a gas is ( 20^{circ} mathrm{C} ) and
pressure is changed from ( boldsymbol{P}_{1}=mathbf{1} . mathbf{0} times )
( 10^{5} P a ) to ( P_{2}=1.65 times 10^{5} P a ) and the
volume is changed by ( 10 % ). The bulk modulus is:
A ( .1 .55 times 10^{5} P a )
В. ( 1.15 times 10^{5} P a )
c. ( 1.4 times 10^{5} P a )
D. ( 1.01 times 10^{5} mathrm{Pa} )
11
23When a rubber cord is stretched, the change in volume with respect to change in its linear dimensions is negligible. The Poisson’s ratio for rubber
is
( A )
B. 0.25
( c cdot 0.5 )
D. 0.75
11
24Two opposite forces ( F_{1}=120 N ) and
( F_{2}=80 N ) act on an elastic plank of
modulus of elasticity ( boldsymbol{Y}=boldsymbol{2} times )
( 10^{11} N m^{2} ) and length ( l=1 m ) placed
over a smooth horizontal surface. The
cross-sectional area of the planck is ( S=0.5 m^{2}, ) the change in length of the
plank is ( boldsymbol{x} times mathbf{1 0}^{-9} boldsymbol{m} )
A . 1.0
B. 1.5
c. ( 1 . )
D. 1.
11
25A ( 14.5 mathrm{kg} ) mass, fastened to the end of a steel wire of unstretched length ( 1.0 mathrm{m} ) is whirled in a vertical circle with an
angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of
the wire is ( 0.065 mathrm{cm}^{2} ). Calculate the
elongation of the wire when the mass is at the lowest point of its path.
11
26( A ) and ( B ) are two steel wires and the
radius of ( A ) is twice that of ( B ), if they are stretched by the same load, then the stress on B is
A. Four times that of A.
B. Two times that of A
c. Three times that of ( A )
D. Same as that A.
11
27The limit upto which the stress is directly proportional to strain is called
A. elastic limit
B. elastic fatigue
c. elastic relaxation
D. breaking limit
11
28A metal wire of length 1 m and crosssection area ( 2 m m^{2} ) and Young’s
modulus of elasticity ( boldsymbol{Y}=mathbf{4} times )
( 10^{11} N / m^{2} ) is stretched by ( 2 m m . ) Then
A. the restoring force developed in the wire is 1600 N
B. the energy density in the wire is ( 4 times 10^{5} mathrm{J} / mathrm{m}^{3} )
c. the restoring force developed in the wire is 400 N
D. the total elastic energy stored in the wire is ( 1.6 ~ J )
11
29If ( S ) is stress and ( Y ) is Young’s modulus
of material of wire, then energy stored in the wire per unit volume is:
( mathbf{A} cdot 2 S^{2} Y )
в. ( frac{s}{Y x} )
c. ( frac{2 Y}{S^{2}} )
D. ( frac{s^{2}}{2 Y} )
11
30Q Type your question.
surrounded by an incompressible liquid in a cylindrical container. A massless
piston of area ( A ) floats on the surface of
the liquid. The magnitude of fractional change in the radius of the sphere ( left(frac{d R}{R}right) ) when a mass ( M ) is placed slowly on the
piston to compress the liquid is:
( ^{mathrm{A}} cdot frac{M g}{3 A B} )
в. ( frac{M g}{A B} )
c. ( frac{3 M g}{A B} )
D. none of thes
11
31Q Type your question
shown in Fig. The cross sectional area of
( A ) is half that of ( B ) and the Youngs
modulus of ( A ) is twice that of ( B . A )
weight ( mathrm{W} ) is hung as shown. The value of
( x ) so that ( W ) produces equal stress in
wires ( A ) and ( B ) is
( A cdot frac{L}{3} )
в. ( L ) ( overline{2} )
c. ( frac{2 L}{3} )
D. ( frac{3 L}{4} )
11
32Substances that elongate considerably and undergo plastic deformation before they break are known as
A. brittle substances
B. breakable substances
c. ductile substances
D. all of these
11
33According to Hooke’s Law, the elongation produced in a body is :
A. proportional to the force applied
B. inversely proportional to the force applied
c. constant
D. independent of the force applied
11
34A steel wire of length ( L ) and area of cross-section A shrinks by ( Delta l ) during
night. Find the tension developed at
night if Young’s modulus is ( Y ) and wire is clamped at both ends
A. ( frac{A Y L}{Delta l} )
в. ( A Y L )
c. ( A Y Delta l )
D. ( frac{A Y Delta l}{L} )
11
35A uniform steel rod of length 1 m and
area of cross section ( 20 mathrm{cm}^{2} ) is hanging
from a fixed support. Find the increase in the length of the rod. ( left(Y_{text {steel}}=2.0 timesright. )
( mathbf{1 0}^{11} boldsymbol{N m}^{-2}, boldsymbol{rho}_{text {steel}}=mathbf{7 . 8 5} times )
( left.10^{3} K g m^{-3}right) )
A ( .1 .923 times 10^{-5} mathrm{cm} )
В. ( 2.923 times 10^{-5} mathrm{cm} )
c. ( 1 . .123 times 10^{-5} mathrm{cm} )
D. ( 3.123 times 10^{-5} mathrm{cm} )
11
36The delay in recovery on removal of the
deforming force is called
11
37A student performs an experiment to determine the Young’s modulus of a wire, exactly ( 2 mathrm{m} ) long, by Searle’s method. In a particular reading, the student measures the extension in the
length of the wire to be ( 0.8 m m ) with an
uncertainty of ( pm 0.05 mathrm{mm} ) at a load of exactly ( 1.0 k g . ) The student also
measures the diameter of the wire to be
( 0.4 m m ) with an uncertainty of ±0.01
( mathrm{mm} . ) Take ( mathrm{g}=9.8 mathrm{m} / mathrm{s}^{2} ) (exact). The
Young’s modulus obtained from the reading is
в. ( (2.0 pm 0.2) times 10^{11} mathrm{N} / mathrm{m}^{2} )
c. ( (2.0 pm 0.1) times 10^{11} mathrm{N} / mathrm{m}^{2} )
D. ( (2.0 pm 0.05) times 10^{11} mathrm{N} / mathrm{m}^{2} )
11
38Length of a wire is increased by ( 1 mathrm{mm} ) on the application of a given load. If same load is applied to another wire of same material but of length and radius twice that of the first then increase in its
length will be
( mathbf{A} cdot 2 m m )
в. ( frac{1}{2} m m )
( mathrm{c} .4 mathrm{mm} )
D. ( frac{1}{4} m m )
11
39A metal wire upon excess stress moves
to a region of permanent set. Before yielding to the fracture stress, it undergoes an extension equal to twice its length in its plastic region. The nature of the metal is
A . Brittle
B. Ductile
c. Perfectly elastic
D. Perfectly plastic
11
40The bulk modulus of elasticity with increase in pressure
A. increases
B. decreases
c. remains constant
D. increases first up to certain limit and then decreases
11
41A gas undergoes a process in which its pressure ( P ) and volume ( V ) are related as
( boldsymbol{V} boldsymbol{P}^{n}= ) constant. The bulk modulus for
the gas in this process is:
A . np
B. ( p^{1 / n} )
c. ( frac{p}{n} )
D. ( p^{n} )
11
42short steel rods each of cross-sectional
( operatorname{area} 5 c m^{2} . ) The lower ends of ( A ) and ( B )
are welded to a fixed plate ( C D . ) The
upper end of ( A ) is welded to the ( L- )
shaped piece ( boldsymbol{E F G}, ) which can slide
without friction on upper end of ( boldsymbol{B} . mathbf{A} )
horizontal pull of ( 1200 N ) is exerted at
( G ) as shown. Neglect the weight of ( boldsymbol{E F G} )
Longitudinal stress in ( boldsymbol{A} ) is
A. Tensile in nature and having magnitude ( 180 N / m^{2} )
B. Tensile in nature and having magnitude ( 240 N / m^{2} )
c. compressive in nature and having magnitude ( 180 N / c m^{2} )
D. Compressive in nature and having magnitude ( 240 N / c m^{2} )
11
43The force-extension graph of a metal
wire is shown.

At which point on the graph does the metal wire stop obeying Hooke’s law?

11
44The steel wire can withstand a load up
to ( 2940 mathrm{N} ). A load of ( 150 mathrm{kg} ) is suspended from a rigid support. The maximum angle through which the wire can be displaced from the mean position so that the wire does not break
A . 30
B. 60
( c .80 )
D. ( 85^{circ} )
11
45One end of a uniform wire of length ( boldsymbol{L} ) and of weight ( W ) is attached rigidly to a
point in the roof and ( W_{1} ) weight is suspended from looser end. If ( A ) is area
of cross-section of the wire, the stress in the wire at a height ( frac{L}{4} ) from the upper end is
( mathbf{A} cdot frac{W_{1}+W}{a} )
B. ( frac{W_{1}+3 W / 4}{a} )
c. ( frac{W_{1}+W / 4}{a} )
D. ( frac{4 W_{1}+3 W}{a} )
11
46A wire fixed at the upper end stretches by length ( l ) by applying a force ( F ). The work done in stretching is:
( ^{A} cdot frac{F}{2 l} )
в. ( F l )
c. ( frac{2 F}{l} )
D. ( frac{F l}{2} )
11
47Modulus of rigidity is defined as the ratio of
A . Longitudinal stress to longitudinal strain
B. Volumetric stress to volumetric strain
c. shear stress to shear strain
D. Linear stress to linear strain
11
48If the temperature of a wire of length
( 2 m ) area of cross-section ( 1 mathrm{cm}^{2} ) is
increased from ( 0^{circ} C ) to ( 80^{circ} C ) and is not
allowed to increase in length, then force
required for it is ( left{boldsymbol{Y}=mathbf{1 0}^{mathbf{1 0}} boldsymbol{N} / boldsymbol{m}^{2}, boldsymbol{alpha}=right. )
( left.10^{-6} /^{o} Cright} )
A . ( 80 N )
в. ( 160 N )
c. ( 400 N )
D. ( 120 N )
11
49If the compressibility of water is ( sigma ) (sigma) per unit atmospheric pressure, then the decrease in volume V due to ( p )
atmospheric pressure will be :
A. ( sigma V / p )
в. ( sigma p V )
( mathbf{c} cdot sigma / p V )
D. ( sigma p / V )
11
50A metallic rod of length ( l ) and cross
sectional area ( A ) is made of a material
of Young modules ( Y ). If the rod is
elongated by an amount ( y, ) then the work done is proportional to
A ( . y )
B. ( frac{1}{y} )
c. ( y^{2} )
D. ( frac{1}{y^{2}} )
11
51The stress-strain curve shows a
straight line along the third quadrant
What does it depict
A. Elongation in the negative ( x ) – direction
B. compression
c. Negative Youngs modulus
D. Decreasing stress
11
52The maximum load a wire can
withstand without breaking, when its length is reduced to half of its original length, will
A. be double
B. be half
c. be four times
D. remains same
11
53When the rubber band is stretched, it
heats up and it cools down if it is suddenly released. This is depicted using
A. the area under the hysteresis curve
B. the x intercept of the hysteresis curve
c. the y intercept of the hysteresis curve
D. the saturation point of the hysteresis curve
11
54The length of a wire increases by ( 1 % ) on loading a ( 2 k g ) weight on it. Calculate the linear strain in the wire.11
55What is the density of lead under a pressure of ( 2.0 times 10^{8} N / m^{2}, ) if the bulk
modulus of lead is ( 8.0 times 10^{9} N / m^{2} )
Also, the initial density of lead is ( 11.4 g / c m^{3} )
A ( cdot 12.89 g / c m^{3} )
в. ( 14 g / mathrm{cm}^{3} )
c. ( 11.69 g / c m^{3} )
D. Zero
11
56Which of the following affects the elasticity of a substance?
A. Hammering and annealing
B. Change in temperature
c. Impurity in substance
D. All of the above
11
57An ideal spring with a pointer attached to its end, hangs next to a scale. With a ( 100 mathrm{N} ) weight attaches and in
equilibrium, the pointer indicates ’40 on the scale as shown. Using a ( 200 mathrm{N} ) weight instead in’60’ on the scale. Using
an unknown weight ‘X’ instead results in ’30’ on the scale. The value of X is
( A cdot 80 N )
B. 60 N
( c cdot 50 N )
D. ( 40 mathrm{N} )
11
58A wire of cross-sectional area ( 4 times 10^{-4} m^{2} )
modulus of elasticity ( 2 times 10^{11} N / m^{2} )
and length ( 1 m ), is stretched between two
vertical rigid poles. A mass of ( 1 mathrm{kg} ) is suspended at its center. If the angle it makes with the horizontal is ( frac{1}{2} times 10^{-x} ) rad. Find ( x )
11
59The diagram shows stress v/s strain
curve for the materials ( A ) and ( B ). From
the curve we infer that
A. A is brittle but B is ductile
B. A is ductile but B is brittle
c. Both A and B are ductile
D. Both A and B are britlle
11
60The shearing strain is equivalent to
A. Tensile strain + compression strain
B. Tensile strain – compression strain
C. Shear strain + tensile strain
D. Shear strain + compression strain
11
61Which of the following is not dimension less
A. Poission ratio
B. Sharing strain
c. Longitudinal strain
D. Volume stress
11
62Two wires are made of the same
material and have the same volume.
However wire 1 has cross-sectional area
( A ) and wire 2 has cross-sectional area 3
A. If the length of wire 1 increased by ( Delta x ) on applying force ( F, ) how much force is
needed to stretch wire 2 by the same
amount?
A ( .4 F )
в. ( 6 F )
( c .9 F )
D. ( F )
11
63A wire that obeys Hooke’s law is
of length ( l_{1} ) when it is in equilibrium
under a tension ( F_{1} ). Its length becomes ( l_{2} ) when the tension is increased of ( F_{2} )
The energy stored in the wire during this process is
B – ( frac{1}{4}left(F_{2}+F_{1}right)left(l_{2}-l_{1}right) )
c. ( frac{1}{4}left(F_{2}-F_{1}right)left(l_{2}-l_{1}right) )
D – ( frac{1}{2}left(F_{2}-F_{1}right)left(l_{2}-l_{1}right) )
11
64An iron rod of length ( 2 m ) and cross-
sectional area of ( 50 mathrm{mm}^{2} ) stretched by
( 0.5 m m, ) when a mass of ( 250 k g ) is hung from its lower end. Young’s modulus of iron rod is
A ( cdot 19.6 times 10^{20} N / m^{2} )
В. ( 19.6 times 10^{18} mathrm{N} / mathrm{m}^{2} )
C. ( 19.6 times 10^{10} N / m^{2} )
D. ( 19.6 times 10^{15} N / m^{2} )
11
65f the brass wire were replaced by
another brass wire of diameter 1 m ( m )
where should the mass be suspended
so that ( A B ) would remain horizontal?
( mathbf{A} cdot x=0.06 m )
В . ( x=0.12 ) т
c. ( x=0.24 m )
D. ( x=0.48 m )
11
66One end of a slack wire (Youngs
modulus ( Y, ) length ( L ) and cross
sectional area ( A ) ) is clamped to a rigid wall and the other end to a block (mass
m) which rests on a smooth horizontal
plane. The block is set in motion with a speed v. What is the maximum
distance the block will travel after the
wire becomes taut?
A ( cdot v sqrt{frac{m L}{A Y}} )
B. ( v sqrt{frac{2 m L}{A Y}} )
c. ( v sqrt{frac{m L}{2 A Y}} )
D ( cdot L sqrt{frac{m v}{A Y}} )
11
67The lower edge of a square slab of side ( 50 mathrm{cm} ) and thickness ( 20 mathrm{cm} ) is rigidly
fixed to the base of a table. A tangential force of ( 30 mathrm{N} ) is applied to the slab. If the shear moduli of the material is ( 4 times )
( 10^{10} N / m^{2}, ) then displacement of the
upper edge, in maters is?
A ( .4 times 10^{-12} )
В. ( 4 times 10^{-10} )
c. ( 6 times 10^{-10} )
D. ( 6 times 10^{-12} )
E . ( 8 times 10^{-10} )
11
68Two wires of same material and same
diameter have lengths in the ratio 2: 5 They are stretched by the same force. The ratio of work done in stretching them is :
A .5: 2
B. 2:5
( c cdot 1: 3 )
D. 3:
11
69Define Young’s modulus.11
70A toy cart is tied to the end of an
unstretched string of length ‘L’. When revolved, the toy card moves in
horizontal circle with radius ‘2 ( l ) ‘ and
time period ( T . ) If it is speeded until it moves in horizontal circle of radius ‘3 ( l^{prime} )
with period ( T_{1}, ) relation between ( T ) and
( T_{1} ) is (Hooke’s law is obeyed)
( ^{mathbf{A}} cdot_{T_{1}}=frac{2}{sqrt{3}} T )
в. ( T_{1}=sqrt{frac{3}{2}} T )
( ^{mathbf{c}} cdot_{T_{1}}=sqrt{frac{2}{3}} T )
( T_{1}=frac{sqrt{3}}{2} T )
11
71Hooke’s law holds good up to
A. Plastic point
B. Limit of proportionality
c. Breaking point
D. None of these
11
72The formula that relates Bulk’s
modulus with poisson’s ratio is
В. ( Y=3 B(1-sigma) )
c. ( Y=3 B(1-2 sigma) )
D. ( Y=3 B(1+sigma) )
11
73The work performed (in J) to make a
hoop out of a steel band of length ( l= )
( 2.0 m, ) width ( h=6.0 mathrm{cm}, ) and thickness
( boldsymbol{delta}=mathbf{2 . 0} boldsymbol{m m} ) is ( boldsymbol{x} times mathbf{1 0}^{mathbf{1}} boldsymbol{J} . ) The process
is assumed to proceed within the elasticity range of the material. Find the
value of ( boldsymbol{x} )
11
74Six identical uniform rods
( P Q, Q R, R S, S T, T U ) and ( U P ) each
weighing ( mathrm{W} ) are freely joined at their
ends to form a hexagon. The rod ( P Q ) is
fixed in a horizontal position and
middle points of ( boldsymbol{P Q} ) and ( boldsymbol{S T} ) are
connected by a vertical string. The tension in string is
( A cdot W )
В. ( 3 W )
( c .2 W )
0.44
11
75The bulk modulus of a metal is
( 10^{10} N / m^{2} ) and Poisson’s ratio ( 0.20 . ) If average distance between the
molecules is ( 3 A ) then the inter
atomic force constant :
A. ( 5.4 N / m )
в. ( 7.5 N / m )
c. ( 7.6 N / m )
D. 30N/m
11
76The increase in pressure required in ( k P a, ) to decrease the 200 litres volume
of a liquid by ( 0.004 % ) is (bulk modulus of the liquid ( =2100 M P a) )
A . 8.4
B. 84
c. 92.4
D. 16
11
77When a body undergoes a linear tensile strain if experience a lateral contraction also. The ratio of lateral
contraction to longitudinal strain is known as
A. Young’s modulus
B. Bulk modulus
c. Poisson’s law
D. Hooke’s law
11
78Doubling the thickness of the wire
A. doubles the young’s modulus of the wire
B. halves the young’s modulus of the wire
C. keeps the young’s modulus constant
D. decreases the young’s modulus of the wire by ( 1 / 8 ) th
11
79Energy per unit volume in a stretched wire is equal to
A. half of load x strain
B. loadx strain
c. stress ( times ) strain
D. half of stress ( x ) strain
11
80A stress ( 10^{7} ) Pa produces a strain of ( 4 x )
( 10^{-3} . ) The energy stored per unit volume
of the body ( left(operatorname{in} mathrm{J} . mathrm{m}^{-3}right) ) is
( A cdot 2 times 10^{3} )
B. ( 2 times 10^{4} )
c. ( 2.5 times 10^{10} )
D. ( 0.8 times 10^{4} )
11
81Hardness is the resistance of a metal to
the penetration of another harder body
which does not
A. have poisson’s ratio less than 0
B. receive a permanent set.
c. have low young’s modulus
D. have high elastic point
11
82Which of the following is the graph showing stress-strain variation for
elastomers?
(1)
(2)
(3)
(4)
11
83Ratio of transverse to axial strain is
A. Toricelli ratio
B. Poisson’s ratio
c. Stoke’s ratio
D. Bernoulli’s ratio
11
84What is Poisson’s ratio?11
85Assertion (A) : Silver is a ductile
material, Reason (R): For a ductile material yield point and breaking point are separated by larger distance than for brittle
materials on the stress-strain curve.
A. Both assertion and reason are true and the reason is correct explanation of the assertion
B. Both assertion and reason are true, but reason is not correct explanation of the assertion
c. Assertion is true, but the reason is false
D. Assertion is false, but the reason is true
11
86Which of the following is/are true about deformation of a material?
A. Deformation capacity of the plastic hinge and resilience of the connections are essential for goodd plastic behavior
B. Deformation capacity equations considering yield stress and gradient of moment
c. Different materials have different deformation capacity
D. All of the above
11
87Which of the following is a type of deformation?

This question has multiple correct options
A. Strain
B. Stress
c. Fracture
D. All of the above

11
88Assertion
The stress-strain behaviour varies from
material to material.
Reason
A rubber can be pulled to several times its original length and still returns to its
original shape.
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
89To determine the Young modulus of a wire, several measurements are taken.
In which row can the measurement not
be taken directly with the stated apparatus?
A. measurement: area of cross-section of wire apparatus : micrometer screw gauge
B. measurement: extension of wire ; apparatus: vernier scale
c. measurement: mass of load applied to wire ; apparatus : electronic balance
D. measurement: original length of wire ; apparatus metre rule
11
90A sphere of radius ( R ) is submerged in
water completely, what force should be
imparted to the sphere, so that every point in it experiences a constant volume stress
A. Force should be proportional to ( R )
B. Force should be proportional to ( 1 / R )
C. Force should be proportional to ( R^{2} )
D. Force should be proportional to ( 1 / R^{2} )
11
91A liquid of bulk modulus ( k ) is
compressed by applying an external pressure such that its density
increases by ( 0.01 % . ) The pressure applied on the liquid is:
A ( cdot frac{k}{10000} )
в. ( frac{k}{1000} )
c. ( 1000 k )
D. ( 0.01 k )
11
92A ( 40 k g ) boy whose leg bones are ( 4 c m^{2} ) in
area and ( 50 mathrm{cm} ) long falls through a
height of ( 50 c m ) without breaking his leg bones. If the bones can stand a stress of
( 0.9 times 10^{8} N / m^{2} . ) Calculate Young’s
Modulus for the material of the bone
11
93Assertion (A): Ductile metals are used
to prepare thin wires. Reason (R) : In the stress-strain curve
of ductile metals, the length between the points representing elastic limit and breaking point is very small.
A. Both (A) and ( ( R ) ) are true and ( ( R ) ) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not correct explanation of (A)
c. (A) is true but (R) is false.
D. (A) is false but (R ) is true
11
94For a given material Young’s modulus is
2.4 times that of its rigidity modulus. Its Poisson’s ratio is
A . 2.4
B. 1.2
( c .0 .4 )
D. 0.2
11
95The fractional change in the volume of oil is 1 percent when a pressure of ( 2 times 10 )
( 7 mathrm{N} / mathrm{m}^{2} ) is applied. The bulk modulus and its compressibility is :
A ( cdot 3 times 10^{8} mathrm{N} / mathrm{m}^{2}, 0.33 times 10^{-9} mathrm{m}^{2} / mathrm{N} )
B. ( 5 times 10^{9} mathrm{N} / mathrm{m}^{2}, 2 times 10^{-10} mathrm{m}^{2} / mathrm{N} )
c. ( 2 times 10^{9} mathrm{N} / mathrm{m}^{2}, 5 times 10^{-10} mathrm{m}^{2} / mathrm{N} )
D. 3 ( times 10^{+9} mathrm{N} / mathrm{m}^{2}, 5 times 10^{-9} mathrm{m}^{2} / mathrm{N} )
11
96Four wires made of same materials are
stretched by the same load. Their dimensions are given below. The one which elongates more is?
A. Wire of length ( 1 mathrm{m} ) and diameter ( 1 mathrm{mm} )
B. Length 2m, diameter 2 mm
c. Length 3m, diameter 3 mm
D. Length 0.5m, diameter 0.5mm
11
97A steel wire of ( 4.0 mathrm{m} ) in length is
stretched through ( 2.0 mathrm{mm} ). The crosssectional area of the wire is ( 2.0 m m^{2} .1 )
Young’s modulus of steel is ( 2.0 times ) ( mathbf{1 0}^{mathbf{1 1}} mathbf{N} / mathbf{m}^{mathbf{2}} ) find
(i) the energy density of
wire
(ii) the elastic potential energy stored in the wire.
11
98A structure steel rod has a radius of
( 10 m m ) and a length of ( 1.0 m . A 100 k N )
force stretches it along its length.
(b) elongation. and Calculate ( ( a ) ) stress.
(c) strain on the rod. Young’s modulus, of stricture steel is ( 2.0 times 10^{11} N m^{-2} )
11
99There are two wires of the same
material. There radii and lengths are
both in the ratio ( 1: 2 . ) If the extensions
produce dare equal, what is the ratio of the loads?
A .1: 2
B . 2: 1
c. 1: 4
D. 4: 1
11
100If the strain in wire is not more than
( 10^{-3} ) and ( Y=4 times 10^{11} N / m^{2}, ) diameter of
wire is ( 1 mathrm{mm} ), then the maximum weight that can be hanged from wire is then:-
( mathbf{A} cdot 157 N )
в. ( 314 N )
c. ( 120 N )
D. ( 160 N )
11
101A steel wire is ( 1 mathrm{m} ) long and ( 1 mathrm{mm}^{2} ) in the
area of cross-section. If it takes ( 200 N )
to stretch the wire by 1 m ( m ), the force that will be required to stretch the wire of the same material and cross-
sectional area from a length of ( 10 m ) to
( 1002 mathrm{cm} )
A. ( 100 N )
B. ( 200 N )
c. ( 400 N )
D. 2000N
11
102topp
( Q )
the atoms are almost lacking in mobility, their kinetic energy is negligibly small. It is this lack of mobility which makes a solid rigid. This rigidity is the cause of elasticity in solids. In some solids such as steel, the atoms are bound together by larger nter-atomic forces than in solids such as aluminum. Thus, the elastic behavio
varies from solid to solid. Even fluids
exhibit elasticity. All material bodies get deformed when subjected to a suitable force. The ability of a body to regain its original shape and size is called elasticity. The deforming force per unit area is called stress. The
change in the dimension (length, shape or volume) divided by the original dimension is called strain. The three kinds of stress are tensile stress
shearing stress, and volumetric stress. The corresponding strains are called tensile strain, shearing strain and volume strain. According to Hooke’s law, within the elastic limit, stress is proportional to strain. The ratio stress/strain is called the modulus of
elasticity. The figure shows the strain-stress graphs for materials A and B. From the graph it follows that:
A. material A has a higher Young’s mod
B. material B has a higher Young’s modulus than
( c )
es
for
11
103If ( S ) is stress and ( Y ) is the Young’s modulus of the material of a wire, the
energy stored in the wire per unit volume is :
( mathbf{A} cdot 2 S^{2} Y )
B. ( frac{s^{2}}{2 Y} )
c. ( frac{2 Y}{S^{2}} )
D. ( frac{s}{2 Y} )
11
104The increase in the length of a wire on stretching is ( 0.025 % ). If its Poisson’s
ratio is ( 0.4, ) then the percentage decrease in the diameter is :
A . 0.01
B. 0.02
c. 0.03
D. 0.04
11
105Write Copper, Steel, Glass and Rubber in order of increasing coefficient of elasticity
A. Steel, Rubber, Copper, Glass
B. Rubber. Copper, Glass, Steel
c. Rubber. Glass, steel, Copper
D. Rubber. Glass, copper, Steel
11
106According to Hooke’s law of elasticity, if stress is increased, then the ratio of
stress to strain :
A. becomes zero
B. remains costant
c. decreases
D. increases
11
107The length of a wire under stress changes by ( 0.01 % . ) The strain produced is
A ( cdot 10^{-4} )
B. 0.01
c. 1
D. ( 10^{4} )
11
108The value of ( tan (90-theta) ) in the graph
gives :
A. Young’s modulus of elasticity
B. compressibility
c. Shear strair
D. Tensile strength
11
109Two blocks of masses ( m ) and ( M=2 m )
are connected by means of a metal wire of cross sectional area ( A ), passing over a frictionless fixed pulley as shown in figure. The system is then released. The stress produced in the wire is :
( A cdot frac{m g}{A} )
в. ( frac{2 m g}{3 A} )
( c )
11
110The elastic limit of an elevator cable is
( 2 times 10^{9} N / m^{2} . ) The maximum upward
acceleration that an elevator of mass
( 2 times 10^{3} k g ) can have when supported by
a cable whose cross-sectional area is
( 10^{-4} m^{2}, ) provided the stress in cable would not exceed half of the elastic
limit would be
A ( cdot 10 m s^{-2} )
B. ( 50 m s^{-2} )
( mathrm{c} cdot 40 mathrm{ms}^{-2} )
D. Not possible to move up
11
111A ball falling in a lake of depth ( 200 mathrm{m} ) shows ( 0.1 % ) decrease in its volume at
the bottom. What is the Bulk modulus
of the ball material? (Take density of water ( =1000 mathrm{kg} / mathrm{m}^{3} ) ):
A ( cdot 19.6 times 10^{8} N / m^{2} )
В. ( 19.6 times 10^{-10} mathrm{N} / mathrm{m}^{2} )
c. ( 19.6 times 10^{10} N / m^{2} )
D. ( 19.6 times 10^{-8} N / m^{2} )
11
112The modulus of elasticity ( (boldsymbol{E}) ) and modulus of rigidity ( (C) ) are related by(m is the poissons ratio)
( ^{A} cdot C=frac{E}{3(m-2)} )
в. ( c=frac{E}{2(m+1)} )
( c cdot c=frac{3(m-2)}{m E} )
D. ( c=frac{2(m+1)}{m E} )
11
113A material has poisson’s ratio ( 0.5 . ) If ( a ) uniform rod of it suffers a longitudinal
strain of ( 3 times 10^{-3}, ) what will be
percentage increase in volume?
A . २%
B. 3%
c. 5%
D. 0%
11
114In Young’s double slit experiment, the two equally bright slits are coherent, but of phase difference ( frac{pi}{3} . ) If maximum
intensity on the screen is ( I_{0} ), the intensity
at the point on the screen equidistant from the slits is_-
A . ( I_{0} )
в. ( frac{I_{0}}{2} )
c. ( frac{I_{0}}{4} )
D. ( frac{3 I_{0}}{4} )
11
115A rod of mass ( ^{prime} M^{prime} ) is subjected to force
( t^{prime} ) and ( ^{prime} 2 f^{prime} ) at both the ends as shown in
the figure. If young modulus of
its material is ‘ ( y^{prime} ) and its length is ( L )
find total elongation of rod.
A ( cdot frac{f l}{2 A y} )
в. ( frac{f l}{A y} )
c. ( frac{3 f l}{2 A v} )
D. ( frac{4 f l}{2 A y} )
11
116A piece of copper having a rectangular
cross-section of ( 15.2 mathrm{mm} times 19.1 mathrm{mm} ) is
pulled in tension with ( 44,500 mathrm{N} ) force, producing only elastic deformation. Calculate the resulting strain?
11
117One end of a string of length ( L ) and cross-sectional area ( A ) is fixed to a
support and the other end is fixed to a bob of mass ( m ). The bob is revolved in a
horizontal circle of radius ( r ) with an
angular velocity ( omega ) such that the string makes an angle ( theta ) with the vertical. The stress in the string is :
A. ( frac{m g}{A} )
в. ( frac{m g}{A}left(1-frac{r}{L}right) )
c. ( frac{m g}{A}left(1+frac{r}{L}right) )
D. none of these
11
118Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0. What is the maximum
tension,that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed ( 6.9 times 10^{7} ) pa ?
Assume that each rivet is to carry onequarter of the load
( A cdot 3 )
в. 2.5
( c cdot 4 )
D. 5
11
119Which one of the following is true about Bulk Modulus of elasticity?
A. It is the ratio of compressive stress to volumetric strain
B. It is the ratio of compressive stress to linear strain
c. It is the ratio of tensile stress to volumetric strain
D. It is the ratio of tensile stress to linear strain
11
120Figure shows the stress-strain graphs
for materials ( A ) and ( B ).
From the graph it follows that:
This question has multiple correct options
A. material A has a higher Young’s modulus
B. material B is more ductile
( c . ) material A is more brittle
D. material A can withstand a greater stress
11
121The diameter of a brass rod is ( 4 m m ) and
Youngs modulus of brass is ( 9 times ) ( 10^{10} N / m^{2} ) The force required to stretch
it by ( 0.1 % ) of its length is
A. ( 360 pi N )
Then
в. ( 36 N )
c. ( 144 pi times 10^{3} N )
D. ( 36 pi times 10^{5} N )
11
122A rod has poisson’s ratio ( 0.2 . ) If a rod
suffers a longitudinal strain of ( 2 times 10^{-3} )
then the percentage change in volume
is
( mathbf{A} cdot+0.12 )
в. -0.12
c. 0.28
D. -0.28
11
123toppr
Q Type your question
Those of which not regaining are called
plastic. There may be delay in the
regaining in some materials. They are
said to have got elastic aftereffect,
since they have gone beyond the elastic
limit. Repeated application and removal
of force break at any point time and so
a re avoided.
The stress strain graph for two
materials ( A ) and ( B ) is shown in the
following figure:

The time in which the two materials
regain their original status is ( t_{A} ) and ( t_{B} )
related as ( t_{B}=2 t_{B} . ) Then the materia
under elastic aftereffect (relatively) is
( mathbf{A} cdot B )
B. ( A )
( c cdot operatorname{Both} A ) and ( B )
D. Neither ( A ) nor ( B )

11
124When an elastic material with Young’s modulus ( Y ) is subjected to stretching stress ( mathrm{S} ), elastic energy stored per unit volume of the material is
( ^{A} cdot frac{Y S}{2} )
B. ( frac{S^{2} Y}{2} )
c. ( frac{s^{2}}{2 Y} )
D. ( frac{s}{2 Y} )
11
125Two wires of the same material and
length but diameter in the ratio 1: 2 are
stretched by the same load. The ratio of
elastic potential energy per unit volume for the two wires is:
A . 1: 1
B . 2: 1
c. 4: 1
D. 16: 1
11
126A force of ( 10^{3} mathrm{N} ) stretches the length of a
hanging wire by 1 millimeter. The force required to stretch a wire of same material and length but having four
times the diameter by 1 millimeter is :
( mathbf{A} cdot 4 times 10^{3} mathrm{N} )
В ( cdot 16 times 10^{3} mathrm{N} )
c. ( frac{1}{4} times 10^{3} mathrm{N} )
D. ( frac{1}{16} times 10^{3} mathrm{N} )
11
127Which of the following are correct?
This question has multiple correct options
A. The product of bulk modulus of elasticity and compressibility is 1
B. A rope 1cm in diameter breaks if the tension in it exceeds ( 500 N ). The maximum tension that may be
given to a similar rope of diameter ( 2 mathrm{cm} ) is ( 2000 mathrm{N} )
C. According to Hooke’s law, the ratio of the stress and strain remains constant
D. None of the above
11
128For a constant hydraulic stress on an object, the fractional change in the object’s volume ( (Delta V / V) ) and its bulk modulus (B) are related as:
A ( cdot frac{Delta V}{V} propto B )
B. ( frac{Delta V}{V} propto frac{1}{B} )
c. ( frac{Delta V}{V} propto B^{2} )
D. ( frac{Delta V}{V} propto B^{-2} )
11
129The shape of the string is drawn at ( t=0 )
and the area of the pulse enclosed by the string and the ( x ) -axis is measured. It
will be equal to
( mathbf{A} cdot 2 c m^{2} )
B. ( 2.5 mathrm{cm}^{2} )
c. ( 4 mathrm{cm}^{2} )
D. ( 5 mathrm{cm}^{2} )
11
130Two wires of same material & length
are stored by the same force. Their masses are in the ratio 3: 2 . Find ratio of
their elongation
11
131Let ( Y_{S} ) and ( Y_{A} ) represent Young’s modulus for steel and aluminium
respectively lt is said that steel is more elastic than aluminium. Therefore, it
follows that
A. ( Y_{S}=Y_{A} )
в. ( Y_{S}Y_{A} )
( stackrel{Y_{S}}{Y_{A}}=0 )
11
132When a certain weight is suspended from a long uniform wire, its length increases by ( 1 mathrm{cm} ). If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, the
increase in length will be
( mathbf{A} cdot 0.5 mathrm{cm} )
B. ( 2 c m )
( c .4 c m )
D. 8 cm
11
133A wire of initial length ( L ) and radius ( r ) is stretched by a length ( l ). Another wire of same material but with initial length ( 2 L ) and radius ( 2 r ) is stretched by a
length ( 2 l ). The ratio of the stored elastic energy per unit volume in the first and second wire is,
( A cdot 1: 4 )
B. 1: 2
c. 2: 1
D. 1:
11
134Bulk modulus of water is ( 2 times 10^{9} N / m^{2} )
The change in pressure required to increase the density of water by ( 0.1 % ) is
A. ( $ $ 21 ) times ( 10^{wedge}{9} N /left{m^{wedge}{2} $ $right. )
B. $$21times 10^283N/ {mwedge(2) $$
c. ( $ $ 21 ) times ( 10^{wedge}{6} N /left{m^{wedge}(2) $ $right. )
D. $$21times 10^{223N/ } { m ^ { wedge } ( 2 ) $ $
11
135For which range, during unloading the
above curve will be retraced?
A. up to ( O A ) only
B. up to ( O B )
c. up to ( C )
D. never retraced its path
11
136When a force is applied on a wire of uniform cross-sectional area ( 3 times )
( 10^{-6} m^{2} ) and length ( 4 m, ) the increase in
length is 1 ( m m . ) Energy stored in it will
be ( left(Y=2 times 10^{11} N / m^{2}right) )
A . ( 6250 J )
в. 0.177 Л
c. ( 0.075 J )
D. ( 0.150 J )
11
137Which of the following is a proper
sequence?
A. proportional limit, elastic limit, yielding, failure
B. elastic limit, proportional limit, yielding, failure
C . yielding, proportional limit, elastic limit, failure
D. proportional limit, yielding, elastic limit, failure
11
138The Young’s modulus of the material of a wire is ( 6 times 10^{12} N / m^{2} ) and there is no
transverse in it, then its modulus of rigidity will be
A ( cdot 3 times 10^{12} N / m^{2} )
В . ( 2 times 10^{12} N / m^{2} )
C ( cdot 10^{12} N / m^{2} )
D. None of the above
11
139Copper of fixed volume ‘V’ is drawn into
wire of length ‘I’. When this wire is
subjected to a constant force ‘F’, the
extension produced in the wire is ( ^{prime} Delta l^{prime} ) Which of the following graph is a straight line?
A ( cdot Delta l v s frac{1}{l} )
B. ( Delta l v s l^{2} )
c. ( Delta l v s frac{1}{l^{2}} )
D. ( Delta l ) vs ( l )
11
140Determine the value of ( x ) so that equal
stresses are produced in each wire.
A ( .1 .33 m )
3. ( 2.5 mathrm{m} )
( c .3 .6 m )
D. ( 2.1 m )
11
141If the ratio of lengths, radii and Youngs
modulii of steel and brass wires in the
figure are a, b and c respectively. Then the corresponding ratio of increase in
their lengths would be:
A ( cdot frac{2 a}{h^{2}} )
в. ( frac{3 a}{2 b^{2} c} )
c. ( frac{3 c}{2 a b^{2}} )
D. ( frac{2 a^{2}}{b} )
11
142The increase in pressure required to decrease the 200 litres volume of a
liquid by ( 0.004 % ) in kPa is : (bulk modulus of the liquid ( =2100 M P a) )
A . 8.4
B. 84
c. 92.4
D. 168
11
143If both the wires are pulled for the same extension, then:
A. ( W_{A}>W_{B} )
в. ( W_{A}<W_{B} )
( mathbf{c} cdot T_{A}<T_{B} )
D ( cdot Y_{A}<Y_{B} )
11
144To determine the Young’s modulus of a wire, the formula is ( Y=frac{F}{A}, frac{L}{triangle l} ; ) where
( boldsymbol{L}= )length( , boldsymbol{A}=operatorname{area~of~cross-section~} )
of the wire, ( triangle boldsymbol{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 . 1
B. 10
c. ( 0 . )
D. 0.01
11
145An aluminium rod has a breaking strain ( 0.2 % . ) The minimum cross-sectional
area of the rod in ( m^{2} ) in order to support
a load of ( 10^{4} N ) is if (Young’s modulus is
( mathbf{7} times mathbf{1 0}^{mathbf{9}} mathbf{N m}^{-mathbf{2}} mathbf{)} )
( mathbf{A} cdot 1.7 times 10^{-4} )
В. ( 1.7 times 10^{-3} )
c. ( 7.1 times 10^{-4} )
D. ( 1.4 times 10^{-4} )
11
146A uniform rod of length L and mass M is pulled horizontally on a smooth surface
with a force F. Determine the elongation
of rod if Young’s modulus of the
material is ( Y )
11
147A structural steel rod has a radius of
( 10 m m ) and a length of ( 1.0 m . A 100 k N )
force stretches it along its length. Calculate (a) stress,
(b) elongation, and
(c) strain on the rod. Young’s modulus,
of structural steel is ( 2.0 times 10^{11} N m^{2} )
11
148The bulk modulus of elasticity for monoatomic ideal gas during an isothermal process is ( (mathrm{P}= ) pressure of the gas)
A. ( P )
в. ( frac{2 P}{3} )
c. ( frac{5 P}{3} )
D. ( frac{7 P}{3} )
11
149Which of the following shafts is stronger
A. solid
B. hollow
c. cylindrical
D. circular
11
150For a perfectly rigid body
A. Young’s modulus is infinite and bulk modulus is zero
B. Young’s modulus is zero and bulk modulus is infinite
C. Young’s modulus is infinite and bulk modulus is also infinite
D. Young’s modulus is zero and bulk modulus is also
zero
11
151Hooke’s law states that under normal
conditions
A. Stress is inversely proportional to strain till elastic limit
B. Stress is directly proportional to strain till elastic limit
C. Stress is independent of strain
D. Stress is proportional to elastic modulus
11
152A rubber ball is brought into ( 200 mathrm{m} ) deep water, its volume is decreased by ( 0.1 % ) then volume elasticity coefficient of the material of ball will be:
( left(text {Given } rho=10^{3} k g / m^{3} text { and } g=right. )
( left.9.8 m s^{-2}right) )
A ( cdot 19.6 times 10^{8} N / m^{2} )
В. ( 19.6 times 10^{-10} N / m^{2} )
c. ( 19.6 times 10^{10} N / m^{2} )
D. ( 19.6 times 10^{-8} N / m^{2} )
11
153A student plots graph from his readings on the determination of Young’s modulus of a metal wire but forgets to
put the labels (figure). The quantities
on ( X ) and ( Y ) -axes respectively may be
This question has multiple correct options
A. weight hung and length increased
B. stress applied and length increased
c. stress applied and strain developed
D. length increased and the weight hung
11
154A ball of mass ‘m’ drops from a height ‘h which sticks to mass-less hanger after
striking. Neglect overturning, find out the maximum extension in the rod.
Assuming rod is massless
11
155Find the increase in pressure required to decrease the volume of water sample
by ( 0.01 % ). Bulk modulus of water ( = ) ( 2.1 times 10^{9} N m^{-2} )
A ( cdot 4.3 times 10^{4} N / m^{2} )
B. ( 1.8 times 10^{7} N / m^{2} )
c. ( 2.1 times 10^{5} N / m^{2} )
D. ( 3.7 times 10^{4} N / m^{2} )
11
156A metal wire is stretched by a load. The force-extension graph is shown. What is represented by the area under
the whole graph?
A. The change in gravitational potential energy of the wirt
B. The energy that would be released from the wire if the final load was removed
c. The energy transferred into heat energy in the wire
D. The work done in stretching the wire
11
157In a wire stretched by hanging a weight from its end, the elastic potential energy per unit volume in terms of the
longitudinal strain ( sigma ) and modulus of
elasticity ( boldsymbol{Y} ) is
A ( cdot frac{Y sigma^{2}}{2} )
в. ( frac{Y sigma}{2} )
( ^{text {c. }} frac{2 Y sigma^{2}}{2} )
D. ( frac{Y^{2} sigma}{2} )
11
158A wire of length ( L ) has a linear mass
density ( mu ) and area of cross-section ( boldsymbol{A} )
and Young’s modulus ( Y ) is suspended vertically from a rigid support. If the
mass ( M ) is hung at the free end of the
wire, then the extension produced in the
wire is:
( ^{mathbf{A}} cdot frac{mu g L^{2}+M g L}{2 Y A} )
( ^{mathbf{B}} cdot frac{2 mu g L^{2}+M g L}{2 Y A} )
c. ( frac{mu g L^{2}+2 M g L}{2 Y A} )
( frac{mu g L^{2}+M g L}{Y A} )
11
159A cube of wood supporting ( 200 g m )
mass just in water ( (rho=1 g / c c) . ) When
the mass is removed, the cube rises by ( 2 c m . ) The volume of cube is
A . ( 1000 c c )
B. ( 800 c c )
c. ( 500 c c )
D. None of these
11
160A beam of cross section area ( A ) is made
of a material of Young modulus Y. The beam is bent into the arc of a circle of
radius R. The bending moment is proportional to
A ( cdot frac{Y}{R} )
в. ( frac{Y}{R A} )
c. ( frac{R}{Y} )
D. ( Y R )
11
161A wire of initial length ( L ) and radius ( r ) is
stretched by a length ( l ). Another wire of same material but with initial length ( 2 L ) and radius ( 2 r ) is stretched by a
length ( 2 l ). The ratio of stored elastic
energy per unit volume in the first and
second wire is:
A .1: 4
B. 1: 2
c. 2: 1
D. 1: 1
11
162A stress strain curve plotted for two
wires are as shown. The labels 1 is the
elastic point, 2 and 3 are the yield
points wires ( A ) and ( B ). Which one is more
ductile
4.4
B. B
c. Both are brittle
D. Both are ductile
11
163Which of the following relations is not
correct?
A ( cdot frac{Y}{eta}=2(1+sigma) )
в. ( frac{Y}{3 K}=1-2 sigma )
c. ( _{Y}=frac{9 K eta}{3 K+eta} )
D. ( frac{Y}{eta}+frac{Y}{3 K}=3 )
11
164A ball of radius ( R ) and with bulk
modulus of elasticity ( K ) is kept in a liquid inside a cylindrical container. It is pressed by putting a mass ( mathrm{m} ) on a massless piston of cross-sectional area
A, then the fractional decrease in the
radius of ball will be
A ( cdot frac{M g}{3 K R} )
в. ( frac{M g}{3 K A} )
c. ( frac{M g}{K A} )
D. ( frac{M g K}{3 A R} )
11
165If the longitudinal strain in a cubical body is three times the lateral strain then the bulk modulus ( K, ) Young’s modulus ( Y ) and rigidity ( eta ) are related by
This question has multiple correct options
A. ( K=Y )
в. ( eta=frac{3 Y}{8} )
c. ( Y=frac{3 eta}{8} )
D. ( Y=eta )
11
166Which one of the following is the unit of compressibility
A ( cdot m^{3} / N )
B . ( m^{2} / N )
( mathrm{c} cdot m^{2}-N )
D. ( m / N )
11
167The Young’s modulus of steel is twice that of brass. Two wires of sample
length and of same area of cross section, one of steel and another of
brass are suspended from the same
roof. If we want the lower ends of the
wires to be at the same level, then the
weights added to the steel and brass wires must be in the ratio of:
A. 1: 1
B. 1: 3
c. 2: 1
D. 4: 1
11
168A composite wire consits of a steel wire of length ( 1.5 ~ m ) and a copper wire of
length ( 2.0 m, ) with a uniform cross-
sectional area of ( 2.5 times 10^{-5} m^{2} . ) It is
loaded with a mass of 200 kg. Find the
extension produced. Young’s modulus of copper is ( 1.0 times 10^{11} N m^{-2} ) and that of
steel is ( 2.0 times 10^{11} N m^{-2} )
Take ( boldsymbol{g}=mathbf{9 . 8} boldsymbol{m} boldsymbol{s}^{-2} )
11
169Discuss the behavior of wire under
increasing load
11
170The stress-strain plot for wires made of two materials (I and II) is presented
schematically in the accompanying
figure. The points ( C_{I} ) and ( C_{I I} ) represent
fracture points of the two materials
and II respectively. It can be concluded
from these graphs that
A. material I has Young’s modulus larger than that of materia
B. the linear region of material I extends to a larger valu of stress than that of material II
c. both materials I and II are equally brittle
D. material l is more ductile than materia
11
171The plasticity behaviour of a material
determines the
A. elastic behavior of the material
B. resistance of the material to electric fields
C. viscous behavior of the material and is irrecoverable.
D. resistance of the material to magnetic fields
11
172Determine the pressure required to reduce the given volume of water by ( 2 % ) Bulk modulus of water is ( 2.2 times )
( 10^{4} N m^{-2} )
A ( cdot 4.4 times 10^{7} mathrm{Nm}^{-2} )
В. ( 2.2 times 10^{7} N m^{-2} )
c. ( 3.3 times 10^{7} mathrm{Nm}^{-2} )
D. ( 1.1 times 10^{7} N m^{-2} )
11
173The stress ( (y) ) and the strain ( (x) ) are measured for a wire by adding loads to one end of the wire and the other end suspended. They follow an equation ( y=3 x+1 ) from ( x=0 ) to 3 and ( y=-4(x- )
3) ( ^{2}+10 ) for ( x>3 ). In which region is
Hooke’s law valid
A ( . x=0 ) to 3
B. ( x=3 )
( c cdot x>3 )
D. for all values of ( x )
11
174A solid sphere of radius ( 20 mathrm{cm} ) is
subjected to a uniform pressure of ( 10^{6} )
( N m^{-2} . ) If the bulk modulus is ( 1.7 times )
( 10^{11} N m^{-2}, ) the decrease in the volume
of the solid is approximately equal to:
A ( cdot 0.2 mathrm{cm}^{3} )
В. ( 0.3 mathrm{cm}^{3} )
( mathrm{c} cdot 0.4 mathrm{cm}^{3} )
D. ( 0.5 mathrm{cm}^{3} )
11
175A metal string is fixed between rigid supports. It is initially at negligible tension. Its Young’s modulus is ( Y ) density is ( rho ) and coefficient of linear
expansion is ( alpha ). It is now cooled
through a temperature ( t, ) transverse
waves will move along it with a speed of
A ( cdot sqrt{frac{Y alpha t}{rho}} )
B ( cdot Y sqrt{frac{alpha t}{rho}} )
c. ( alpha sqrt{frac{Y t}{rho}} )
D ( cdot t sqrt{frac{rho}{Y alpha}} )
11
176Copper of fixed volume ‘v; is drawn into wire of length ‘I. When this wore is subjected to a constant force ‘F’, the
extension produced in the wire is ‘ ( Delta l ) Which of the following graphs is a straight line?
A ( cdot Delta l ) versus ( frac{1}{i} )
B. ( Delta l ) versus ( l^{2} )
c. ( Delta l ) versus ( frac{1}{l^{2}} )
D. ( Delta l ) versus ( l )
11
177The valve ( V ) in the bent tube is initially
kept closed. Two soap bubbles ( boldsymbol{A} )
(smaller) and ( B ) (larger) are formed at
the two open ends of the tube. ( V ) is now
opened and air can flow freely between
the bubbles.
A. There will be no change in the size of the bubbles
B. The bubbles will become of equal size
c. ( A ) will become smaller and ( B ) will become larger
D. The sizes of ( A ) and ( B ) will be interchanged
11
178The property required for propagation of
transverse wave is :
A. longitudinal strain
B. lateral strain
c. shearing strain
D. poisson’s ratio
11
179The theoretical limits of poisson’s ratio lies between -1 to 0.5 because
A. Shear modulus and bulk’s modulus should be positive
B. Bulk’s modulus is negative during compression
c. Shear modulus is negative during compression
D. Young’s modulus should be always positive
11
180Two identical wires are suspended from a roof, but one is of copper and other is of iron. Young’s modulus of iron is thrice that of copper. The weights to be added on copper and iron wires so that the ends are on the same level
must be in the ratio of
A .1: 3
B. 2:
c. 3: 1
D. 4: 1
11
181Three fluids 1,2 and 3 have Bulk Moduli
of ( k 1, k 2 ) and ( k 3 ) respectively. If ( k 1>k 2> )
k3, which liquid will have the highest compressibility
A . liquid 1
B. liquid 2
c. liquid 3
D. theyll have equal compressibilities
11
182The dimensions of two wires ( A ) and ( B )
are the same. But their materials are
different, Their load- extension
graphs are shown. If ( Y_{A} ) and ( Y_{B} ) are the
values of Young’s modulus of elasticity
of ( A ) and ( B ) respectively then :
A. ( Y_{A}>Y_{B} )
В. ( Y_{A}<Y_{B} )
( mathbf{c} cdot Y_{A}=Y_{B} )
( mathbf{D} cdot Y_{B}=2 Y_{A} )
11
183A wire is stretched ( 1 mathrm{mm} ) by a force of 1
kN. How far would a wire of the same
material and length but of four times that diameter he stretched by the same force?
( ^{mathbf{A}} cdot frac{1}{2} mathrm{mm} )
в. ( frac{1}{4} mathrm{mm} )
c. ( frac{1}{8} mathrm{mm} )
D. ( frac{1}{16} mathrm{mm} )
11
184Two wires, one of copper and other of
steel of equal length are suspended by the given load. The area of cross section of copper is twice that of steel. What will
be the ratio of the stress in copper to steel wires
( A cdot 2 )
B. 4
( c .0 .25 )
D. 0.5
11
185Find the increase in pressure required to decrease the volume of a water
sample by ( 0.01 % . ) Bulk modulus of
water ( =2.1 times 10^{9} N m^{-2} )
11
186airplane shaped cars attached to steel
rods. Each rod has a length of ( 20.0 mathrm{m} )
and a cross-sectional area of ( 8.00 mathrm{cm}^{2} )
Young’s modulus for steel is ( 2 times )
( 10^{11} N / m^{2} )
When operating, the ride has a
maximum angular speed of ( sqrt{19 / 5} ) rad/s. How much is the rod stretched (in
( mathrm{mm} ) ) then?
A . ( 0.38 mathrm{mm} )
B. ( 0.55 mathrm{mm} )
( c cdot 0.45 mathrm{mm} )
D. 0.34
11
187A piece of copper wire has twice the radius of steel wire. One end of the
copper wire is joined to one end of steel wire so that both of them can be
subjected to the same longitudinal force. ( Y ) for steel is twice that of copper.
When the length of copper wire is increased by ( 1 % ), the steel wire will be stretched by
A . 2% of its original length
B. 1% of its original length
c. ( 4 % ) of its original length
D. 0.5% of its original length
11
188Calculate the diameter of the brass
wire
A ( .2 .1 times 10^{-4} mathrm{m} )
3. ( 4.2 times 10^{-4} mathrm{m} )
c. ( 8.4 times 10^{-4} mathrm{m} )
D. ( 16.8 times 10^{-4} mathrm{m} )
11
189Two wires of the same material and
Iength but diameter in the ratio 1: 2 are stretched by the same force. The ratio of
potential energy per unit volume for the two wires when stretched will be :
A . 1:
B. 2:
( c cdot 4: 1 )
D. 16: 1
11
190A mass ( M ) attached to a spring oscillates with a period of 2 seconds. If
the mass is increased by ( 2 k g ), the
period increases by 1 second. Find the initial mass, assuming that Hooke’s law is obeyed.
11
191A wire is subjected to a longitudinal
strain of ( 0.05 . ) If its material has a
Poisson’s ratio ( 0.25, ) the lateral strain
experienced by it is
A. 0.00625
B. 0.125
c. 0.0125
D. 0.0625
11
192State Hooke’s law, with graphical representation?11
193Change in shape of a body caused by the application of stress is called:
A . rigidity
B. elasticity
c. sheer
D. deformation
11
194An iron bar (Young’s modulus ( = ) ( left.10^{11} N / m^{2}, alpha=10^{-6} /^{circ} Cright) 1 m ) long and
( 10^{-3} m^{2} ) in area is heated from ( 0^{circ} C ) to
( 100^{circ} mathrm{C} ) without being allowed to bend
or expand. Find the compressive force in newtons developed inside the bar
11
195Define the term malleability11
196ends so that it lies horizontally and
without tension. A weight ( W ) is
suspended from the middle point of the wire. The vertical depression is
(Young’s modulus is ( Y ).)
A ( cdot sqrt{frac{2 T l^{2}}{4 A Y}+frac{T^{2} l^{2}}{4 A^{2} Y^{2}}} )
B. ( sqrt{frac{2 T l^{2}}{4 A Y}-frac{T^{2} l^{2}}{4 A^{2} Y^{2}}} )
c. ( sqrt{frac{2 T l^{2}}{4 A Y}} )
D. ( frac{T l}{2 A Y} )
11
197Equal torsional torques act on two rods X and Y having equal length but the
diameter of ( Y ) is twice that wire ( X . ) If ( theta_{x} )
and ( theta_{y} ) are angles of twist,
A ( cdot theta_{x}=frac{1}{2} theta_{y} )
в. ( quad theta_{x}=frac{1}{4} theta_{y} )
( mathbf{c} cdot_{theta_{y}}=frac{theta_{x}}{8} )
D. ( _{theta_{y}}=frac{1}{16} theta_{x} )
11
198Suppose the object in figure shown is the brass plate of an outdoor sculpture.
If experiences shear forces as a result of
an earthquake. The frame is ( 0.80 m ) and
( 0.50 c m ) thick. Calculate the shear
strain produced in this object if the
displacement x is 0.16mm (Shear
modulus=( left.3.5 times 10^{10} P aright) )
11
199Young’s modulus of a metal is ( 15 times 10^{11} )
Pa. If its poisson’s ratio is ( 0.4 . ) The bulk modulus of the metal in ( P a ) is :
A ( cdot 25 times 10^{11} )
В . ( 2.5 times 10^{11} )
c. ( 250 times 10^{11} )
D. ( 0.25 times 10^{11} )
11
200A metal cylinder of length ( L ) is
subjected to a uniform compressive
force ( F ) as shown in the figure. The
material of the cylinder has Young’s modulus ( Y ) and Poisson’s ratio ( sigma ). The
change in volume of the cylinder is:
( ^{mathrm{A}} cdot frac{sigma F L}{Y} )
B. ( frac{(1-sigma) F L}{Y} )
( c )
( D )
11
201A wire elongates by I mm when a load ( mathbf{W} ) is hanged from it. If the wire goes over a pulley and two weights Weach are hung at the two ends,the elongation of the wire will be (in mm)
A. zero
B. I / 2
( c )
D. 2
11
202Two wires of the same material and
length but diameters in the ration 1: 2
are stretched by the same force. The potential energy per unit volume for the two wires when stretched will be in the
ratio :
( mathbf{A} cdot 16: 1 )
B . 4: 1
c. 2: 1
D. 1: 1
11
203Poisson’s ratio of a material is 0.5
applied to wire of this material, these in
the cross-section area increase in the
length is.
11
204The length of a metal wire is ( L_{1} ) when
the tension is ( T_{1} ) and ( L_{2} ) when the
tension is ( T_{2} . ) The unstretched length of
wire is :
A ( cdot frac{L_{1}+L_{2}}{2} )
в. ( sqrt{L_{1} L_{2}} )
c. ( frac{T_{2} L_{1}-T_{1} L_{2}}{T_{2}-T_{1}} )
D. ( frac{T_{2} L_{1}+T_{1} L_{2}}{T_{2}+T_{1}} )
11
205Two exactly similar wires of steel ( (mathrm{y}=20 ) ( x 10^{11} ) dyne ( / mathrm{cm}^{2} ) ) and copper ( (mathrm{y}=12 times 10 )
11 dyne /cm ( ^{2} ) )are stretched by equal forces. If the total elongation is ( 1 mathrm{cm} ) elongation of copper wire is
( mathbf{A} cdot 3 / 5 mathrm{cm} )
в. ( 5 / 3 c m )
( mathbf{c} cdot 3 / 8 c m )
D. ( 5 / 8 c m )
11
206A copper rod with length ( 1.4 mathrm{m} ) and area
of cross-section of ( 2 mathrm{cm}^{2} ) is fastened to a
steel rod with length L and cross-
sectional area ( 1 mathrm{cm}^{2} . ) The compound rod
is subjected to equal and opposite pulls
of magnitude ( 6.00 times 10^{4} mathrm{N} ) at its ends.
What is the strain in each rod? ( left[boldsymbol{Y}_{text {steel}}=right. ) ( left.mathbf{2} times mathbf{1 0}^{11} boldsymbol{P a} ; boldsymbol{Y}_{C U}=mathbf{1 . 1} times mathbf{1 0}^{mathbf{1 1}} boldsymbol{P a}right] )
11
207A material has Poisson’s ratio ( 0.2 . ) If a
uniform rod of its suffers longitudinal
strain ( 4.0 times 10^{-3}, ) calculate the
percentage change in its volume.
A . ( 0.15 % )
B . ( 0.02 % )
c. ( 0.24 % )
D. 0.48%
11
208An air filled balloon is at a depth of ( 2 mathrm{km} )
below the water level in an ocean.
Determine the normal stress on the
balloon [atmospheric pressure ( =10^{5} ) Pa ( ] )
A ( .190 times 10^{5} P a )
В. ( 196 times 10^{5} mathrm{Pa} )
c. ( 190 times 10^{7} P a )
D. ( 196 times 10^{7} P a )
11
209If a rubber ball is taken at the depth of ( 200 m ) in a pool, its voulme decreases by
( 0.1 % ). If the density of the water is ( 1 times ) ( 10^{3} k g / m^{3} ) and ( g=10 m / s^{2}, ) then the
volume elasticity in ( N / m^{2} ) will be
A ( cdot 10^{8} )
B . ( 2 times 10^{8} )
( c cdot 10^{9} )
D. ( 2 times 10^{9} )
11
210A wire suspended vertically is stretched by a ( 20 mathrm{kg} f ). Applied to its free end. The increase in length of the wire is 2 mm. The energy stored in the wire is ( left(g=10 m s^{-2}right) )
B. ( 0.2 J )
c. ( 0.4 J )
D. ( 5 J )
11
211A thick rope of rubber of density ( 1.5 times ) ( 10^{3} mathrm{kg} / mathrm{m}^{3} ) and Young’s modulus ( 5 times )
( 10^{6} mathrm{N} / mathrm{m}^{2}, 8 mathrm{m} ) length is hung from the
ceiling of a room, the increases in its length due to its own weight is :
( left(g=10 mathrm{m} / mathrm{s}^{2}right) )
A ( .9 .6 times 10^{-2} mathrm{m} )
в. ( 19.2 times 10^{-7} mathrm{m} )
c. ( 9.6 times 10^{-7} mathrm{m} )
D. ( 9.6 m )
11
212A steel wire of length ( 4 m ) is stretched by
a force of ( 100 N . ) The work done to
increase the length of the wire by ( 2 m m ) is
A . 0.4 .5
в. ( 0.2 J )
( c .0 .1 J )
D. ( 1 . )
11
213Assertion
Strain causes the stress in an elastic
body
Reason
An elastic rubber is more plastic in
body.
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
214A hydraullic press contains ( 250 l i t ) of oil Find the decrease in volume of the oil
when its pressure increases to ( 10^{7} ) Pa.
The bulk modulus of the oil is ( boldsymbol{K}=mathbf{5} times )
( mathbf{1 0}^{mathbf{5}} boldsymbol{P a} )
A. ( -0.8 l i t )
B. – ( 0.5 l i t )
c. ( -0.6 l i )
D. – ( 0.9 l i t )
11
215Estimate the change in the density of
water in ocean at a depth of ( 400 mathrm{m} )
below the surface. The density of water
at the surface ( =1030 mathrm{kg} m^{-3} ) and the
bulk modulus of water ( =2 times 10^{9} mathrm{N} m^{-2} )
11
216Find the increment in the length of a
steel wire of length ( 5 m ) and radius
6 mm under its own weight.Density of steel ( =8000 k g / m^{3} ) and Young’s
modulus of steel ( =2 times 10^{11} N / m^{2} )
What is the energy stored in the wire? ( left(text { Take } g=9.8 m / s^{2}right) )
11
217A copper rod of ( 88 mathrm{cm} ) and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is :
( left(alpha_{C u}=1.7 times 10^{-5} K^{-1} text {and } alpha_{A l}=right. )
( left.2.2 times 10^{-5} K^{-1}right) )
( mathbf{A} cdot 6.8 mathrm{cm} )
B. ( 113.9 mathrm{cm} )
( mathbf{c} .88 mathrm{cm} )
D. ( 68 mathrm{cm} )
11
218The dimensions of volume strain is:
( mathbf{A} cdot m^{3} )
B . ( 1 / m^{3} )
c. no dimensions
D. ( m^{-} )
11
219A uniform aluminium wire of length ( 3 mathrm{m} )
and area of cross-section ( 2 m m^{2} ) is
extended through 12 mm. The energy stored in the wire is
( boldsymbol{Y}_{boldsymbol{A l}}=boldsymbol{7} times mathbf{1 0}^{mathbf{1 0}} boldsymbol{N} / boldsymbol{m}^{2} mathbf{)} )
A . ( 336 J )
B. 33.6 ( J )
c. ( 3.36 J )
D. 0.336 J
11
220Hooke’s law essentially defines
A. stress
B. strain
c. yeild point
D. elastic limit
11
221A copper wire of length ( 2.2 mathrm{m} ) and a stee
wire of length ( 1.6 mathrm{m} ). both of diameter 3.0
( mathrm{mm}, ) are connected end to end.When
stretched by a load, the net elongation is found to be ( 0.70 mathrm{mm} . ) Obtain the load
applied.
11
222The change in unit volume of a material
under tension with increase in its
poisson’s ratio will be
A. Increase
B. Decrease
c. Remains same
D. Initially increases and then decreases
11
223equal and opposite tensile forces ( F ) at
its ends. Consider a plane through the
bar making an angle ( theta ) with a plane at
right angles to the bar. Then shearing
stress will be maximum if ( boldsymbol{theta} )
( mathbf{A} cdot 0^{circ} )
B ( .30^{circ} )
( mathbf{c} cdot 45^{circ} )
D. ( 60^{circ} )
E .90
11
224Assertion
The maximum stress value below which
the strain is fully recoverable is called the elastic limit.
Reason
All materials are elastic to some extent
but the degree varies.
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
225The Poisson’s ratio of the material of a
wire is0.25. If it is stretched by a force ( F ) the longitudinal strain produced in the
wire is ( 5 times 10^{-4} ). What is the
percentage increase in its volume?
A . 0.2
B. ( 2.5 times 10^{-2} )
c. zero
D . ( 1.25 times 10^{-6} )
11
226A long, thin metal wire is suspended
from a fixed support and hangs
vertically. Masses are suspended from
its lower end.

The load on the lower end is increased
from zero and then decreased again
back to zero.
The diagram shows the force-extension
graph produced
Where on the graph would the elastic limit be found?
A. anywhere between point ( R ) and point ( S )
B. just beyond point ( S )
c. exactly at point ( S )
D. exactly at point ( T )

11
227The stress-strain curves for three wires
of different materials are shown in
figure, where ( P, Q ) and ( R ) are the elastic
limits of the wires. The figure shows
that
A. Elasticity of wire ( P ) is maximum
B. Elasticity of wire ( Q ) is maximum
C. Elasticity of wire ( R ) is maximum
D. None of the above is true
11
228Find the increase in pressure required to decrease volume of mercury by ( 0.001 % ). (Bulk modulus of mercury ( = )
( left.2.8 times 10^{10} N / m^{2}right) )
11
229Consider the following two statements ( A ) and ( B ) and identify the correct answer.
A) When the length of a wire is doubled, the Young’s modulus of the wire is also doubled
B) For elastic bodies Poisson’s ratio is ( + )
Ve and for inelastic bodies Poissons
ratio is -Ve
A. Both A & B are true
B. A is true but B is false
c. ( A ) is true but ( B ) is true
D. Both A & B are false
11
230Let a steel bar of length ( ‘ l ) ‘, breadth ‘b’ and depth ‘d’ be loaded at the centre by a load ‘W’. Then the sag of bending of beam is (Y = Young’s modulus of material of steel)
A ( frac{W l^{3}}{2 b d^{3} Y} )
в. ( frac{W l^{3}}{4 b d^{3} Y} )
c. ( frac{W l^{2}}{2 b d^{3} Y} )
D. ( frac{W l^{3}}{4 b d^{2} Y} )
11
231A ( 8 mathrm{m} ) long string of rubber, having density ( 1.5 times 10^{3} mathrm{kg} / mathrm{m}^{3} ) and young’s
modulus ( 5 times 10^{6} mathrm{N} / mathrm{m}^{2} ) is suspended
from the ceiling of a room. The increase in its length due to its own weight
will be ( left(g=10 mathrm{m} / mathrm{s}^{2}right) )
A. ( 9.6 times 10^{-2} mathrm{m} )
В. ( 19.2 times 10^{-5} mathrm{m} )
c. ( 9.6 times 10^{-3} mathrm{m} )
D. ( 9.6 mathrm{m} )
11
232A uniform wire of length ( 1 ~ m ) and radius
( 0.028 mathrm{cm} ) is employed to raise a stone of
density ( 2500 mathrm{kg} / mathrm{m}^{3} ) immersed in water. Find the change in elongation of wire when the stone is raised out of
water.
( [text {massofstone}=mathbf{5} k g, ) Yofmaterialo
11
233The depression produced at the end of a
( 50 c m ) long cantilever on applying a load is 15 mm. The depression produced at a
distance of ( 30 mathrm{cm} ) from the rigid end will
be
A. 3.24 ( mathrm{mm} )
B. 1.62 ( mathrm{mm} )
c. ( 6.48 mathrm{mm} )
D. 12.96 mm
11
234The elastic limit of steel cable is ( 3.0 times )
( 10^{8} N / m^{2} ) and the cross-section area is
( 4 c m^{2} . ) Find the maximum upward
acceleration that can be given to a ( 900 k g ) elevator supported by the cable if the stress is not to exceed one-third of
the elastic limit.lf your answer is ( x, ) then mark the value of ( frac{x}{5} )
11
235A light rod of length ( 2.00 m ) is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross section
( 10^{-3} m^{2} ) and the other is of brass of
cross-section ( 2 times 10^{-3} m^{2} . ) Find out the
position along the rod at which a weight may be hung to produce.(Youngs modulus for steel is ( 2 times 10^{11} mathrm{N} / mathrm{m}^{2} ) and for
brass is ( 10^{11} mathrm{N} / mathrm{m}^{2} ) )
a) equal stress in both wires
b) equal strains on both wires
A. ( 1.33 m, 1 m )
в. ( 1 m, 1.33 m )
c. ( 1.5 m, 1.33 m )
D. ( 1.33 m, 1.5 m )
11
236A tungsten wire of length ( 20 mathrm{cm} ) is stretched by ( 0.1 mathrm{cm} . ) Find the strain on the wire.
A .0 .002
B. 0.005
( c cdot 0.001 )
D. 0.004
11
237When load is applied to a wire, the extension is 3 mm. The extension in the
wire of same material and length but
half the radius extended by the same load is :
A. ( 0.75 mathrm{mm} )
B. ( 6 m m )
( c .1 .5 m m )
D. ( 12.0 m m )
11
238Time dependent permanent deformation is called
A. Plastic deformation
B. Elastic deformation
c. Creep
D. Anelastic deformation
11
239Which of the following is a proper
sequence?
A. Elastic region, Yielding, Fracture stress, Strain hardening, Necking
B. Elastic region, Yielding, Strain hardening, Necking Fracture stress
C. Elastic region, Strain hardening, Yielding, Necking , Fracture stress
D. Elastic region, Strain hardening, Necking, Yielding, Fracture stress
11
240A sphere of radius ( 1.00 mathrm{cm} ) is placed in
the path of a parallel beam of light of large aperture. The intensity of the light is ( 0.50 W mathrm{cm}^{-2} . ) If the sphere
completely absorbs the radiation falling on it, find the force exerted by the light beam on the sphere.
11
241If a beam of metal supported at the two ends is loaded at the centre, then the depression at the centre will be proportional to
A ( cdot gamma^{2} )
B. ( gamma )
( c cdot frac{1}{gamma} )
D. ( frac{1}{gamma^{2}} )
11
242A wire ( 2 mathrm{m} ) in length suspended vertically stretches by ( 10 mathrm{mm} ) when the mass of ( 10 mathrm{kg} ) is attached to the lower end. The elastic potential energy gain by the wire is? ( left(operatorname{take} g=10 m / s^{2}right) )
A . 0.5
B. 5 J
c. 50
D. 500 J
11
243What are brittle bodies.??11
244toppr
Q Type your question
removed. They are termed as elastic.
Those of which not regaining are called
plastic. There may be delay in the regaining in some materials. They are said to have got elastic aftereffect, since they have gone beyond the elastic limit. Repeated application and removal of force break at any point time and so are avoided.
The stress strain graph for two materials ( A ) and ( B ) is shown in the
following figure:
The strength of the material ( A ) and ( B ) is
( boldsymbol{S}_{A} ) and ( boldsymbol{S}_{B}, ) respectively, while the longevity of plastic behaviour is ( L_{A} ) and
( boldsymbol{L}_{boldsymbol{B}} cdot ) Then
A. ( S_{A}>S_{B}, L_{A}S_{B}, L_{A}>L_{B} )
D. ( S_{A}<S_{B}, L_{A}<L_{B} )
11
245Among solids, liquids and gases, which posses the greatest bulk modulus?
A. Solids
B. Liquids
c. Gases
D. Both solids and liquids
11
246A uniform rod of length ( ^{prime} L^{prime} ) and density
( rho^{prime} ) is being pulled along a smooth floor
with horizontal acceleration ( alpha ) as shown
in the figure. The magnitude of the stress at the transverse cross-section
through the mid-point of the rod is
A ( frac{rho l alpha}{4} )
в. ( 4 rho l ) d
( c cdot 2 rho l )
D. ( frac{rho l alpha}{2} )
11
247A metallic wire is stretched by
suspending a weight to it. If ( alpha^{2} ) is the longitudinal strain and Y is its Young’s modulus of elasticity, then show that the elastic potential energy per unit volume is given by ( 1 / 2 Y^{2} )
11
248( 1 mathrm{cc} ) of water is taken from the surface
to the bottom of a lake having depth 100m. If bulk modulus of water is ( 2.2 times )
( 10^{9} N / m^{2} ) then decrease in the volume
of the water will be
A ( .4 .5 times 10^{-4} c c )
B. ( 8.8 times 10^{-4} c c )
c. ( 2.2 times 10^{-4} c c )
D. ( 1.1 times 10^{-4} c c )
11
249The value of shear stress which is
induced in the shaft due to applied
couple varies
A. from maximum at the centre to the zero at the circumference
B. from zero at the centre to the maximum at the circumference
c. from maximum at the centre to the minimum at the circumference
D. from minimum at the centre to the maximum at the circumference
11
250The area enclosed in a hysteresis loop
is
A. strain energy per unit volume
B. strain energy per unit volume absorbed in each loading cycle
c. strain energy per unit volume released as heat in each loading cycle
D. total strain energy
11
251For a material ( boldsymbol{Y}=mathbf{6 . 6} times mathbf{1 0}^{mathbf{1 0}} boldsymbol{N} / boldsymbol{m}^{2} )
and bulk modulus ( K 11 times 10^{10} N / m^{2} ) then its Poisson’s ratio is:
A . 0.8
B. 0.35
( c .0 .7 )
D. 0.4
11
252The compressibility of water ( 4 times 10^{-5} )
per unit atmospheric pressure. The decrease in volume of 100 cubic
centimeter of water under a pressure of
100 atmosphere will be:
A ( .0 .4 c c )
в. ( 4 times 10^{-5} c c )
c. ( 0.025 c c )
D. ( 0.004 c c )
11
253Calculate the extension of the steel wire
and the energy stored in it.
A . 45 J
в. 4.5 Л
c. ( 0.45 J )
D. 0.045
11
254Modulus of elasticity for a perfectly elastic body is
A. zero
B. Infinity
( c )
D. can have any value
11
255Match the Column I with Column II
Column
(A) A body which regains its original shape after the removal of external forces
(B) A body which does not regain its original shape after the removal Elastic of external forces.
(C) A body which does not show any deformation on applying external forces
(D) The property of the body to regain
(s) Rigid its original configuration when the deforming forces are removed
A. A-q, B-r, C-s, D-p
B. A-p, B-q, C-r, D-s
( c cdot A-r, B-s, c-p, D-q )
D. A-s, B-p, C-q, D-r
11
256Assertion
From the relation ( Y=frac{F l}{A Delta l}, ) we can say
that, if length of a wire is doubled, its
Young’s modulus of elasticity will also
becomes two times.
Reason
Modulus of elasticity is a material
property.
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
257Two boys are holding a horizontal rod of length ( L ) and weight ( W ) through its two ends. If now one of the boys suddenly leaves he rod. what is the instantaneous
reaction force experienced by the other boy?
A ( cdot frac{W}{4} )
в. ( frac{W}{2} )
c. ( frac{3 W}{4} )
D. ( W )
11
258A vertical metal cylinder of radius ( 2 mathrm{cm} )
and length ( 2 m ) is fixed at the lower end and a load of ( 100 k g ) is put on it. Find ( (a) )
the stress
(b) the strain and
(c) the
compression of the cylinder. Young modulus of the metal ( =2 times 10^{11} N m^{-2} )
11
259A steel wire of length ( 4 mathrm{m} ) and diameters ( 5 mathrm{mm} ) is stretched by ( 5 mathrm{kg} ) weight find the change in it’s diameter if ( boldsymbol{y}=mathbf{0 . 4} times )
( mathbf{1 0}^{12} boldsymbol{d} boldsymbol{y} boldsymbol{n} e / boldsymbol{c m}^{2} ) and ( boldsymbol{sigma}=mathbf{0 . 3} )
11
260Work done in stretching a wire through ( 1 mathrm{mm} ) is ( 2 J . ) What amount of work will
be done for elongating another wire of same material, with half the length and
double the radius of cross section, by 1 ( mathrm{mm} ? )
A .2
в. 4
c. 8 J
D. 16
11
261When the tension in a metal wire is ( T_{1} )
its length is ( l_{1}, ) when the tension is ( T_{2} )
its length is ( l_{2} ). The natural length of
wire is :
A. ( T_{1} l_{1}+T_{2} l_{2} )
в. ( frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} )
( overbrace{frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}+T_{1}}}^{text {in }} )
D. ( frac{T_{2}}{T_{1}}left(l_{1}+l_{2}right) )
11
262If the volume of a wire remains constant
when subjected to tensile stress, the value of Poisson’s ratio of the material
of the wire is:
A . ( 0 . )
B. 0.2
( c .0 .4 )
D. 0.5
11
263Two wires ( A ) and ( B ) of same length are made of same material. The figure represents the load F versus extension
( Delta x ) graph for the two wires. Then:
A. the cross sectional area of A is greater than that of B.
B. the elasticity of B is greater than that of A.
C. the cross-sectional area of B is greater than that of A.
D. the elasticity of A is greater than that of B.
11
264A tension of ( 22 mathrm{N} ) is applied to a copper
wire of cross-sectional area ( 0.02 mathrm{cm}^{2} )
Young’s modulus of copper is ( 1.1 times ) ( 10^{11} N / m^{2} ) and Poisson’s ratio ( 0.32 . ) The
decrease in cross sectional area will be:
A ( cdot 1.28 times 10^{-6} mathrm{cm}^{2} )
в. ( 1.6 times 10^{-6} mathrm{cm}^{2} )
c. ( 2.56 times 10^{-6} mathrm{cm}^{2} )
D. ( 0.64 times 10^{-6} mathrm{cm}^{2} )
11
265A thin metal sheet is being bent by or pounded in to a new shape. The process of being elastic to plastic behaviour is known as
A. Yield
B. Creep
c. welding
D. Tinkering
11
2663. The adjacent graph shows the extra extension (Ax) of a
wire length 1 m suspended from the top of a roof at one
end with an extra load AW connected to the other end.
If the cross-sectional area of the
Alx10 m)
wire is 10-m?, calculate the
Young’s modulus of the material of 4
the wire.
(a) 2 x 10′ N/m²
2 —
(b) 2 x 10-11 N/m?
>W(N)
(c) 3 x 1013 N/m
0 20 40 60 80
(d) 2 x 1016 N/m²
11
267Assertion
(A): Steel is more elastic than
rubber.
Reason (R): Under a given deforming force, steel is deformed less than rubber.
A) Both Assertion and Reason are true and the reason is correct explanation of
the assertion
B)Both Assertion and Reason are true,
but reason is not correct explanation of the assertion
C) Assertion is true, but the reason is
false
D) Assertion is false, but the reason is
true
( A cdot A )
B. B
( c cdot c )
( D cdot D )
11
268As compared to concrete, steel has compressive strength:
A. 25 times less
B. equal
c. 25 times more
D. 5 times more
11
269A tension of ( 20 N ) is applied to a copper
wire of cross sectional area ( 0.01 c m^{2} )
Young’s Modulus of copper is ( 1.1 times )
( 10^{11} N / m^{2} ) and Poisson’s ratio is 0.32
The decrease in cross sectional area of
the wire is:
( mathbf{A} cdot 1.16 times 10^{-6} mathrm{cm}^{2} )
В. ( 1.16 times 10^{-5} mathrm{m}^{2} )
c. ( 1.16 times 10^{-4} m^{2} )
D. ( 1.16 times 10^{-3} mathrm{cm}^{2} )
11
270The load versus elongation graph for four wires of the same materials is
shown in the figure The thinnest wire is
represented by the line
A. ( 0 c )
B. OD
( c cdot O A )
D. OB
11
271Linear elastic deformation is governed
by
A. Hooke’s Law
B. Euler Bernoulli’s equation
c. both
D. none
11
272The volume change of a solid copper
cube ( 10 c m ) on an edge, when subjected
to a pressure of ( 7 M P a ) is then (Bulk modulus of copper ( =140 G P a) )
A ( .5 times 10^{-2} mathrm{cm}^{3} )
В. ( 10 times 10^{-2} mathrm{cm}^{3} )
( mathbf{c} cdot 15 times 10^{-2} c m^{3} )
D. ( 20 times 10^{-2} mathrm{cm}^{3} )
11
273If the potential energy of a spring is ( V ) on stretching it by ( 2 mathrm{cm} ) then its potential energy when it is stretched by ( 10 mathrm{cm} ) will be
A. v/25
B. 5 v
c. v/ 5
D. 25 V
11
274A 10 meter long thick rubber pipe is suspended from one of its ends. The extension produced in the pipe under its own weight will be ( :(Y=5 times )
( 10^{6} N / m^{2} ) and density of rubber ( = )
( left.1500 k g / m^{3}right) )
( mathbf{A} cdot 1.5 m )
B. ( 0.15 mathrm{m} )
( mathrm{c} .0 .015 mathrm{m} )
D. ( 0.0015 mathrm{m} )
11
275The graph is drawn between the applied force ( F ) and the strain ( (x) ) for a thin
uniform wire. The wire behaves as
a liquid in the part:
( A cdot a b )
B. bc
( c cdot c d )
D. oa
11
276The ratio of shearing stress to the shearing strain is defined as
A. Young’s modulus
B. bulk modulus
c. shear modulus
D. compressibility
11
277Assertion: Stress is the internal force
per unit area of a body Reason: Rubber is more elastic than
stee
A. If both assertion and reason are true but the reason is the correct explanation of assertion.
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false.
E. If reason is true but assertion is false
11
278One end of a uniform rope of length and of weight ( w ) is attached rigidly to a
point in the roof and a weight ( mathbf{w}_{1} ) is suspended from its lower. If s is the area
of cross-section of the wire, the stress in the wire at a height ( frac{3 L}{4} ) from its lower end is:
A ( cdot frac{w}{s} )
B. ( frac{w_{1}+frac{w}{4}}{s} )
c. ( underbrace{w_{1}+frac{2 w}{4}}_{s} )
D. ( frac{w_{1}+w}{s} )
11
279According to Hooke’s law of elasticity, if stress is increased, then the ratio of
stress to strain :
A. becomes zero
B. remains constant
c. decreases
D. increases
11
280A cube at temperature ( 0^{circ} C ) is
compressed equally from all sides by an
external pressure ( P . ) By what amount should its temperature be raised to bring it back to the size it had before
the external pressure was applied. The bulk modulus of the material of the
cube is ( B ) and the coefficient of linear
expansion is ( alpha )
( mathbf{A} cdot P / B a )
в. ( P / 3 B alpha )
c. ( 3 pi alpha / B )
D. ( 3 B / P )
11
281A wire ( left(Y=2 times 10^{11} N / mright) ) has length
( 1 m ) and area ( 1 m m^{2} . ) The work required
to increased its length by ( 2 m m ) is
A. ( 400 J )
B. ( 40 J )
c. ( 0.4 J )
D. ( 0.04 J )
11
282Two rods ( A ) and ( B ). each of equal length
but different materials are suspended from a common support as shown in the figure. The roads ( A ) and ( B ) can support a
maximum load of ( W_{1}=600 mathrm{N} ) and ( W_{2}= ) ( 6000 mathrm{N}, ) respectively. If their cross-
sectional areas are ( A_{1}=10 m m^{2} ) and ( A_{2} )
( =1000 m m^{2}, ) respectively, then identify the stronger material.
11
283If the temperature of a wire of length
( 2 m ) and area of cross section ( 1 mathrm{cm}^{2} ) is
increased from ( 0^{0} C ) to ( 80^{0} C ) and is not
allowed to increase in length, then required for it is ( boldsymbol{Y}=mathbf{1 0}^{mathbf{1 0}} boldsymbol{N} / boldsymbol{m}^{mathbf{2}} )
A. ( 0.008 N )
B. ( 1.06 N )
( c cdot 2 cdot 4 N )
D. ( 3.2 N )
11
284The length of a metal wire is ( l_{1} ) when the tension in it is ( F_{1} ) and ( l_{2} ) when the
tension in it is ( F_{2} ). The natural length of
the wire is
A. ( frac{l_{1} F_{1}+l_{2} F_{2}}{F_{1}+F_{2}} )
в. ( frac{l_{2}-l_{1}}{F_{2}-F_{1}} )
c. ( frac{l_{1} F_{2}-l_{2} F_{1}}{F_{2}-F_{1}} )
D. ( frac{l_{1} F_{1}-l_{2} F_{2}}{F_{2}-F_{1}} )
11
285Assertion
The strain present in the material after
unloading is called the residual strain or plastic strain and the strain
disappears during unloading is termed as recoverable or elastic strain.
Reason
After yieild point, there is some residual stress left in an material on unloading.
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
286The length of a wire of cross-sectional
( operatorname{area} 1 times 10^{-6} m^{2} ) is ( 10 mathrm{m} . ) The young’s
modulus of the material of the wire is
25 G.pa. When the wire is subjected to a tensile force of ( 100 N ), the
elongation produced in ( m m ) is:
A . 0.04
B. 0.4
( c cdot 4 )
D. 40
11
287Find out elongation in a rod Given :
( Y=2 times 1011 mathrm{N} / mathrm{m} 2, mathrm{p}=104 mathrm{kg} / mathrm{m} 3 mathrm{Y}=2 times 1011 mathrm{N} / mathrm{m} )
( 2, p=104 mathrm{kg} / mathrm{m} 3 )
( A .9 m n )
в. ( 10 m m )
( c .18 m m )
D. ( 3 m m )
11
288Assertion
Steel is more elastic than rubber.
Reason
For same strain, steel requires more stress to be produced in it
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
289An Indian rubber cord ( L ) metre long and
area of cross-section ( A ) meter ( ^{2} ) is
suspended vertically. Density of rubber is ( rho k g / ) meter ( ^{3} ) and Young’s modulus of
rubber is ( Y ) Newton/metre ( ^{2} ). If the cord
extends by ( l ) metre under its own
weight, then extension ( l ) is:
( mathbf{A} cdot frac{L^{2} rho g}{Y} )
B. ( frac{L^{2} rho g}{2 Y} )
( ^{mathbf{C}} cdot frac{L^{2} rho g}{4 Y} )
D. ( frac{Y}{L^{2} rho g} )
11
290The Bulk of Ethanol, Mercury and water are given as 0.9,25 and 2.2 respectively in units of ( 10^{8} N m^{-2} ). For a given value
of pressure, the fractional compression in volume is ( triangle V / V . ) Which of the
following statements about ( triangle boldsymbol{V} / boldsymbol{V} ) for
these three liquids is correct?
A. Mercury > Ethanol > Water
B. Ethanol> Mercury > Water
c. water> Ethanol > Mercury
D. Ethanol> Water> Mercury
11
291Two rods of different materials having coefficients of thermal expansion and
Young’s moduli ( Y_{1}, Y_{2}, ) respectively are
fixed between two rigid massive walls. The rods are heated such that undergo the same increase in temperature.
There is no bending of the rods. If ( boldsymbol{alpha}_{1}: )
( boldsymbol{alpha}_{2}=boldsymbol{2}: boldsymbol{3}, ) the thermal stresses
developed in the two rods are equal
provided ( Y_{1}: Y_{2} ) is equal to:
A .2: 3
B. 1: 1
c. 3: 2
D. 4: 9
11
292The elongation of a steel wire stretched
by a force is ‘e’. If a wire of the same material of double the length and half the diameter is subjected to double the force, its elongation will be
A. ( 16 e )
B . ( 4 e )
c. ( left(frac{1}{4}right) e )
D. ( left(frac{1}{16}right) )
11
293What is the meaning of ductility?11
294Two wires ( X ) and ( Y ) are made of different
metals. The Young modulus of wire ( X ) is
twice that of wire Y. The diameter of
wire ( X ) is half that of wire ( Y ).

The wires are extended with the same
strain and obey Hooke’s law.
What is the ratio
A ( cdot frac{1}{8} )
B. ( frac{1}{2} )
( c cdot 1 )
D.

11
295The poisson’s ratio cannot have the value
A. 0.7
B. 0.2
c. ( 0 . )
D. 0.3
11
296A given quantity of an ideal gas is at pressure ( P ) and absolute temperature
T. The isothermal bulk modulus of the
gas is:
A. ( 2 P / 3 )
в. ( P )
c. ( 3 P / 2 )
D. ( 2 P )
11
297Figure shows the strain-stress curve for
a given material. What are
(a) Young’s
modulus and (b) approximate yield
strength for this material?
11
298Distinguish between elastic and plastic
materials.
11
299Plastic deformation in a material
begins at
A. Qpoint
B. Yield point
c. Proportionality limit
D. Elastic limit
11
300The length of metallic wire is ( l_{1} ) when
the tension is ( T_{1} ) and ( l_{2} ) when the
tension is ( T_{1} . ) The original length of the wire is
A ( cdot frac{l_{1}+l_{2}}{2} )
в. ( frac{l_{1} T_{2}+l_{2} T_{1}}{T_{1}+T_{2}} )
c. ( frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} )
D. ( sqrt{T_{1} T_{2} l_{1} l_{2}} )
11
301ILLUSTRATION 33,6 In Searle’s experiment to find Young’s
modulus, the diameter of wire is measured as D = 0.05 cm,
length of wire is L = 125 cm, and when a weight, m = 20.0 kg
is put, extension in wire was found to be 0.100 cm. Find
maximum permissible error in young’s modulus (Y).
11
302A uniform wire (Young’s modulus ( 2 times ) ( left.10^{11} N m^{-2}right) ) is subjected to
longitudinal tensile stress of ( 5 times )
( 10^{7} N m^{-2} . ) If the overall volume change
in the wire is ( 0.02 %, ) the frictional
decrease in the radius of the wire is
close to
A ( .1 .0 times 10^{-4} )
B. ( 1.5 times 10^{-4} )
c. ( 0.25 times 10^{-4} )
D. ( 5 times 10^{-4} )
11
303A tangential force of ( 2100 N ) is applied
on a surface of area ( 3 times 10^{-6} m^{2} ) which
is ( 0.1 m ) from a fixed face. The force
produces a shift of ( 7 mathrm{mm} ) of upper surface with respect to bottom. Th4n
the modulus of rigidity of the material.
В. ( 5 times 10^{10} mathrm{Nm}^{-2} )
c. ( 15 times 10^{10} N m^{-2} )
D. ( 1 times 10^{10} mathrm{Nm}^{-2} )
11
304The diagram shows the change ( x ) in the length of a thin uniform wire caused by the application of stress ( F ) at two
different temperatures ( T_{1} ) and ( T_{2} . ) The
variations shown suggest that:
A ( cdot T_{1}>T_{2} )
в. ( T_{1}<T_{2} )
c. ( T_{1}=T_{2} )
D. None of these
11
305When temperature of a gas is ( 20^{circ} mathrm{C} ) and
pressure is changed from ( p_{1}=1.01 times )
( 10^{5} P a ) to ( p_{2}=1.165 times 10^{5} P a, ) the
volume changes by ( 10 % . ) The bulk modulus is
( mathbf{A} cdot 1.55 times 10^{5} )
B. ( 0.155 times 10^{5} )
C ( .1 .4 times 10^{5} )
D. ( 1.01 times 10^{5} )
11
306A rod of length L and diameter D is subjected to a tensile load P. Which of the following is sufficient to calculate the resulting change in diameter?
A. Youngs modulus
B. Shear modulus
c. Poissons ratio
D. both Youngs modulus and Shear modulus
11
307A ball moving with a velocity v strikes a
wall moving towards the ball with velocity u. An elastic impact lasts for seconds. Find the mean elastic force
acting on the ball
11
308Which of the following statements are
correct?
A. Poisson’s ratio can be greater than 0.5
B. Poisson’s ratio is a characteristic property of the material of the body
C. Poisson’s ratio of a body depends upon its shape and size
D. None of these
11
309A ( 5 k g ) rod of square cross section 5 cm
on a side and 1 m long is pulled along a
smooth horizontal surface by a force
applied at one end. The rod has a
constant acceleration of ( 2 m / s^{2} ) Determine the elongation in the rod.
(Young’s modulus of the material of the
( left.operatorname{rod} text { is } 5 times 10^{3} N / m^{9}right) )
A. Zero, as for elongation to be there, equal and opposite forces must act on the rod
B. Non-zero but cannot be determine from the given situation
( mathbf{c} .4 mu m )
D. ( 16 mu m )
11
310When the intermolecular distance
decreases due to compressive force,
there is :
A. zero resultant force between molecules
B. Repulsive force between molecules
c. Attractive force between molecules
D. No force between molecules
11
311In the stress -strain curve shown, the
metal is
A. Highly Ductile
B. Highly Brittle
c. Highly magnetic
D. Highly chargeable
11
312The property to restore the natural shape or to oppose the deformation is called:
A. elasticity
B. plasticity
c. ductility
D. none of the above
11
313The shape of stress vs strain graph within elastic limit is :
A. parabolic
B. curve
c. straight line
D. ellipse
11
314Which of the following statements is
incorrect?
A. The bulk modulus for solids is much larger than for liquids
B. Gases are least compressible
C. For a system in equilibrium, the value of bulk modulus is always positive
D. The SI unit of bulk modulus is same that of pressure
11
315A rod of mass ( ^{prime} M^{prime} ) is subjected to force
( t^{prime} ) and ( ^{prime} 2 f^{prime} ) at both the ends as shown in
the figure. If young modulus of
its material is ‘ ( y^{prime} ) and its length is ( L )
find total elongation of rod.
A ( cdot frac{f l}{2 A y} )
в. ( frac{f l}{A y} )
c. ( frac{3 f l}{2 A v} )
D. ( frac{4 f l}{2 A y} )
11
316The length of wire increases by ( 9 mathrm{mm} ) when weight of ( 2.5 mathrm{kg} ) is hung from the free end of wire. If all conditions are kept
the same and the radius of wire is made
thrice the original radius, find the increase in length.
11
317Q Type your question
wall. The shearing strength of steel is
( 345 M N / m^{2} . ) The dimensions ( A B=5 )
( mathrm{cm}, mathrm{BC}=mathrm{BE}=2 mathrm{cm} . ) The maximum
load that can be put on the face ABCD
is:(neglect bending of the rod)
( left(g=10 m / s^{2}right) )
A. 3450 kgf
B. 1380 kgf
c. ( 13800 mathrm{kgf} )
D. 345 kgf
E. None of these
11
318The elastic limit of steel is ( 8 x )
( 10^{8} N m^{-2} ) and its Young modulus ( 2 times )
( 10^{11} N m^{-2} . ) Find the maximum
elongation of a half-metre steel wire that can be given without exceeding the elastic limit.
11
319At yield point, Hooke’s law doesn’t hold
good
A. True
B. False
11
320The buckling of a beam is found to be
more if
A. The breadth of the beam is large
B. The beam material has large value of Young’s modulus
c. The length of the beam is small
D. The depth of the beam is small
11
321If Poisson’s ratio ( sigma ) for a material is ( -frac{1}{2} ) then the material is
A. Elastic fatigue
B. Incompressible
c. compressible
D. None of the above
11
322If the elastic limit of copper is ( 1.5 times ) ( 10^{8} N / m^{8}, ) the minimum diameter a
copper wire can have under a load of 10.0 ( k g ), if its elastic limit is not to be exceeded, is ( frac{x}{10} ) mm. Find ( x )
11
323The following four wires of length ( L ) and radius ( r ) are made of the same material
Which of these will have the largest
extension, when the same tension is
applied?
A. ( L=100 mathrm{cm}, r=0.2 mathrm{mm} )
В. ( L=200 c m, r=0.4 m m )
c. ( L=300 c m, r=0.6 m m )
D. ( L=400 mathrm{cm}, r=0.8 mathrm{mm} )
11
324Assertion
Ratio of isothermal bulk modulus and
adiabatic bulk modulus for a
monoatomic gas at a glven pressure is ( frac{3}{5} )
Reason This ratio is equal to ( gamma=frac{C_{p}}{C_{v}} )
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
325An elongation of ( 0.1 % ) in a wire of cross-
section ( 10^{-6} m^{2} ) causes a tension of
( 100 N . Y ) for the wire is
( mathbf{A} cdot 10^{12} N / m^{2} )
B. ( 10^{11} N / m^{2} )
( mathbf{c} cdot 10^{10} N / m^{2} )
D. ( 100 mathrm{N} / mathrm{m}^{2} )
11
326Assertion
Steel is more elastic than rubber.
Reason
For same strain, steel requires more stress to be produced in it
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
327A steel wire of mass ( 3.16 K g ) is
stretched to a tensile strain of ( 1 times 10^{-3} ) What is the elastic deformation energy
if density ( rho=7.9 g / c c ) and ( Y=2 times 10^{11} )
( mathrm{N} / mathrm{m}^{2} ? )
A. ( 4 K J )
в. ( 0.4 K J )
c. ( 0.04 K J )
D. ( 4 J )
11
328For a given material, the Young’s modulus is 2.4 times its modulus of
rigidity. Its Poisson’s ratio is
A . 0.2
B. 0.4
c. 1.2
D. 2.4
11
329A uniform pressure p is exerted on all
sides of a solid cube at temperature
( t^{0} C . ) By what amount should the
temperature of the cube be raised in
order to bring its volume back to the value it had before the pressure was applied? The coefficient of volume expansion of the cube y and the bulk modulus is B.
( mathbf{A} cdot frac{p}{sqrt{2 y} B} )
B. ( frac{p}{2 y B} )
c. ( frac{2 p}{y B} )
D. ( frac{p}{y B} )
11
330If ( mathrm{S} ) is the stress and ( mathrm{Y} ) is Young’s modulus of the material of a wire, the
energy stored in the wire per unit volume is :
( mathbf{A} cdot 2 S^{2} Y )
B. ( frac{s^{2}}{2 Y} )
c. ( frac{2 Y}{S^{2}} )
D. ( frac{S}{2 Y} )
11
331A copper solid cube of ( 60 mathrm{mm} ) side is
subjected to a compressible pressure of ( 2.5 times 10^{7} ) Pa. If the bulk modulus of
copper is ( 1.25 times 10^{11} ) pascals, the change in the volume of cube is
A. ( -43.2 m m^{3} )
В. ( -43.2 m^{3} )
c. ( -43.2 mathrm{cm}^{3} )
D. ( -432 m m^{3} )
11
332A stretched rubber has:
A. increased kinetic energy
B. increased potential energy
C . decreased kinetic energy
D. decreased potential energy
11
333If the work done in stretching a wire by
1 ( m m ) is ( 2 J, ) the work necessary for
stretching another wire of same
material but with double radius of
cross-section and half the length by
1 mm is:
( mathbf{A} cdot 16 J )
B. ( 8 J )
c. ( 4 J )
D ( frac{1}{4} J )
11
334Calculate the work done in stretching steel wire of length ( 2 mathrm{m} ) and of cross sectional area ( 0.0225 m m^{2}, ) when a
load of ( 100 mathrm{N} ) is applied slowly to its free end. (Young’s modulus of steel = 20 x
( mathbf{1 0}^{mathbf{1 0}} mathbf{N} / boldsymbol{m}^{mathbf{2}} mathbf{)} )
11
335what is the ratio of Youngs modulus ( boldsymbol{E} )
to shear modulus ( G ) in terms of
poissons ratio?
( mathbf{A} cdot 2(1+mu) )
B . ( 2(1-mu) )
C ( cdot frac{1}{2}(1-mu) )
D ( cdot frac{1}{2}(1+mu) )
11
336A steel wire if ( 1 ~ m ) long and ( 1 m m^{2} )
cross section area is hanged from rigid end when weight of ( 1 k g ) is hang from it, then change in length will be (Young’s coefficient for wire ( boldsymbol{Y}=mathbf{2} times )
( left.mathbf{1 0}^{mathbf{1 1}} mathbf{N} / boldsymbol{m}^{2}right) )
A. ( 0.5 mathrm{mm} )
B. ( 0.25 mathrm{mm} )
c. ( 0.05 mathrm{mm} )
D. ( 5 m m )
11
337Elasticity is defined as the ability of a
body to
A. Resist linear motion in a hard surface
B. Resist rolling motion in a hard surface
c. Resist a distorting influence and to return to its original size and shape when that influence or force is removed.
D. Resist electric current in a magnetic field
11
338A wire of length ( L ) and cross sectional
area ( A ) is made of a material of Young’s
modulus ( Y ). If the wire is stretched by
an amount ( x, ) the work done is
A ( cdot frac{Y A x^{2}}{3 L} )
в. ( frac{Y A x^{2}}{4 L} )
c. ( frac{Y A x^{2}}{L} )
D. ( frac{Y A x^{2}}{2 L} )
11
339Hookes Laws is used in the
determination of
A. Weight of a body
B. Density of a body
c. volume of body
D. None of these
11
340A wire elongates by 1 m ( m ) when a load Wis hanged from it. If the wire goes over a pulley and two weights Weach are hung at the two ends, the elongation of the wire will be (in ( mathrm{mm} ) ):
A . ( 1 / 2 )
B. 1
( c cdot 2 )
D. zero
11
341The maximum stress that can be
applied to the material of a wire
employed to suspend an elevator is ( frac{3}{pi} times 10^{8} N / m^{2} . ) If the mass of the
elevator is ( 900 mathrm{kg} ) and it moves up with
an acceleration of ( 2.2 m / s^{2} ) then calculate the minimum radius of the
wire.
11
342The pressure that has to be applied to
the ends of a steel wire of length ( 10 c m )
to keep its length constant when its
temperature is raised by ( 100^{circ} mathrm{C} ) is:
(For steel Young’s modulus is ( 2 times )
( 10^{11} N m^{-2} ) and coefficient of thermal
expansion is ( 1.1 times 10^{-5} K^{-1} ) )
A ( cdot 2.2 times 10^{7} ) Ра
B . ( 2.2 times 10^{6} ) ра
c. ( 2.2 times 10^{8} ) Pa
D. ( 2.2 times 10^{9} ) pa
11
343A long spring is stretched by ( 2 mathrm{cm} ) and
its potential energy is ( U . ) If the spring is stretched by ( 10 mathrm{cm} ; ) its potential energy will be (in terms of ( U ) )
A. ( U / 5 )
в. ( U / 25 )
( c .5 U )
D. 25U
11
344Assertion
The stress-strain relationship in elastic region need not be linear and can be
non-linear.
Reason
Steel has non linear,profile in elastic
zone
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
345Find out longitudinal stress and
tangential stress on the given fixed
block
11
346A wire of length L can support a load W. If the wire is broken in to two equal parts then how much load can be suspended by one of those cut wires?
A . Half
B. Same
c. Double
D. One fourth
11
347The energy absorbed in a body, when it
is strained within elastic limits is
known as
A . Resilience
B. Potential energy
c. Kinetic energy
D. Strain energy
11
348When a wire of length ( 10 mathrm{m} ) is subjected
to a force of ( 100 N ) along its length, the
lateral strain produced is ( 0.01 times 10^{-3} )
The Poisson’s ratio was found to be 0.4
If the area of cross-section of wire is
( 0.025 m^{2}, ) its Young’s modulus is:
A ( cdot 1.6 times 10^{8} N / m^{2} )
B . ( 2.5 times 10^{10} N / m^{2} )
c. ( 12.5 times 10^{11} N / m^{2} )
D. ( 16 times 10^{10} N / m^{2} )
11
349The dimensions of strain is:
A. ( L )
B ( cdot L^{2} )
c. It is dimensionless
D. ( M L^{2} T^{-2} )
11
350A solid cylindrical rod of radius ( 3 m m ) gets depressed under the influence of a load through ( 8 m m . ) The depression produced in an identical hollow rod with
outer and inner radii of ( 4 m m ) and ( 2 m m )
respectively, will be
A. 2.7mm
B. ( 1.9 mathrm{mm} )
c. ( 3.2 mathrm{mm} )
D. 7.7mm
11
351A material has Poisson’s ratio ( 0.50 . ) If a
uniform rod of it suffers a longitudinal
strain of ( 2 times 10^{-3}, ) then the percentage
change in volume is
A . 0.6
B. 0.4
( c .0 .2 )
D. zero
11
352Determine the volume contraction of a
solid copper cube, ( 10 mathrm{cm} ) on an edge,
when subject to a hydraulic pressure of ( mathbf{7} times mathbf{1 0}^{mathbf{6}} ) Pa. ( boldsymbol{K} ) for copper ( =mathbf{1 4 0} times mathbf{1 0}^{mathbf{9}} )
( P a )
11
353If a wire is stretched by applying force at one of its ends, then the elastic
potential energy density in terms of Young’s modulus Y and linear strain ( alpha )
will be
( ^{A} cdot frac{alpha Y^{2}}{2} )
в. ( frac{Y alpha}{2} )
c. ( frac{alpha^{2} Y}{2} )
D. ( 2 alpha^{2} Y )
11
354The maximum shear stress induced in
a member which is subjected to an axial load is equal to
A. maximum normal stress
B. half of maximum normal stress
c. twice the maximum normal stress
D. thrice the maximum normal stress
11
355Assertion
The compressive strength of a typical brittle material is significantly higher than its tensile strength.
Reason
In compression force between the
molecules increases.
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
356If the ratio of diameters, lengths and
Young’s modulus of steel and copper wires shown in the figure are ( p, q ) and ( s ) respectively, then the corresponding ratio of increase in their lengths would
be
11
357Shearing strain is expressed by
A. angle of shear
B. angle of twist
c. decrease in volume
D. increase in volume
11
358If the Poisson’s ratio of a solid is ( frac{2}{5}, ) then the ratio of its young’s modulus to the rigidity modulus is
A ( cdot frac{5}{4} )
в. ( frac{7}{15} )
c. ( frac{14}{9} )
D. ( frac{14}{5} )
11
359When a mass is suspended from the end of a wire the top end of which is attached to the roof of the lift, the
extension is ( e ) when the lift
is stationary. If the lift moves up with a constant acceleration ( boldsymbol{g} / mathbf{2}, ) the
extension of the wire would be
A ( cdot frac{2 e}{3} )
в. ( frac{3 e}{2} )
( c cdot 2 e )
D. ( 3 e )
11
360Two wires of the same material have
lengths in the ratio 1: 2 and their radii are in the ratio ( 1: sqrt{2} . ) If they are
stretched by applying equal forces, the increase in their lengths will be in the ratio :
A .2
B . ( sqrt{2}: 2 )
c. 1: 1
D. 1: 2
11
361One end of a uniform rod of mass ( boldsymbol{M} )
and cross-sectional area ( boldsymbol{A} ) is
suspended from the other end. The stress at the mid-point of the rod will be
A ( cdot frac{2 M g}{A} )
в. ( frac{3 M g}{2 A} )
c. ( frac{M g}{A} )
D. zero
11
362There is no change in the volume of a wire due to change in its length on stretching. The Poisson’s ratio of the material of the wire is :
( mathbf{A} cdot+0.50 )
B . -0.50
c. 0.25
D. -0.25
11
363A copper wire ( 3 mathrm{m} ) long is stretched to increase its length by ( 0.3 mathrm{cm} ). Find the lateral strain produced in the wire , if poisson’s ratio for copper is 0.25
A. ( 5 times 10^{-4} )
B. ( 2.5 times 10^{-4} )
c ( .5 times 10^{-3} )
D. ( 2.5 times 10^{-3} )
11
364A steel wire of length ( 7 m ) and cross
section 1 mm( ^{2} ) is hung from a rigid
support with a steel weight of volume 1000 ( c c ) hanging from the other end. Find the decreases in the length of wire, when steel weight is completely immersed in water
( left(boldsymbol{Y}_{text {steel}}=mathbf{2} times mathbf{1 0}^{mathbf{1 1}} mathbf{N} / boldsymbol{m}^{2}right) )
Density of water ( =mathbf{1} boldsymbol{g} / boldsymbol{c} . boldsymbol{c} )
11
365A ( 20 k g ) load is suspended by a wire of
( operatorname{cross} operatorname{section} 0.4 m m^{2} . ) The stress
produced in ( mathrm{N} / mathrm{m}^{2} ) is :
( A cdot 4.9 times 10^{-6} )
B. ( 4.9 times 10^{8} )
( c cdot 49 times 10^{8} )
D. 2.45 times 10 ( ^{-6} )
11
366A wire suspended vertically from one of its ends is stretched by attaching a weight of ( 200 mathrm{N} ) to the lower end. The weight stretches the wire by ( 1 mathrm{mm} ). Then the elastic energy stored in the wire is:
A . 0.1
B. 0.2
c. 10
D. 20
11
367If the work done by stretching a wire by
1 ( m m ) is ( 2 J, ) the work necessary for stretching another wire of the same
material but with half the radius of
cross section and half the length by
1 mm is
( ^{A} cdot frac{1}{4} J )
в. 4.5
c. ( 8 J )
D. 16.5
11
368Assertion
For small deformations, the stress and
strain are proportional to each other
Reason
A class of solids called elastomers does
not obey Hooke’s law.
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
369Four identical hollow cylindrical columns of mild steel support a big
structure of mass 50,000 kg. The inner and outer radii of each column are 30
and ( 60 mathrm{cm} ) respectively. Assuming the load distribution to be uniform,
calculate the compressional strain of each column.
11
370A steel wire of ( 2 m m ) in diameter is
stretched by applying a force of ( 72 N )
Stress in the wire is
A ( cdot 2.29 times 10^{7} N / m^{2} )
B. ( 1.17 times 10^{7} N / m^{2} )
( c )
( 3.6 times 10^{7} N / m^{2} )
D. ( 0.8 times 10^{7} N / m^{2} )
11
371If the elastic deformation energy of a
steel rod of mass ( boldsymbol{m}=mathbf{3 . 1} boldsymbol{k g} ) stretched
to a tensile strain ( varepsilon=1.0 times 10^{-3} ) is ( x )
then value of ( 100 x ) is:
11
372For an elastic material
( mathbf{A} cdot Y>eta )
в. ( Y<eta )
c. ( Y eta=1 )
D. ( Y=eta )
11
373A steel wire of length ( 1 mathrm{m} ) has cross sectional area ( 1 mathrm{cm}^{2} ). If young’s modulus
of steel is ( 10^{11} N / m^{2}, ) then force required to increase the length of wire by ( 1 mathrm{mm} ) will be :
( mathbf{A} cdot 10^{11} N )
В. ( 10^{7} N )
( mathbf{c} cdot 10^{4} N )
D. ( 10^{2} N )
11
374for two materials ( P ) and ( Q ), a student by
mistake puts strain on the y-axis and
stress on the ( x ) -axis as shown in the
figure. Then the correct statement(s) is
(are)
This question has multiple correct options
A. P has more tensile strength than ( Q )
B. P is more ductile than ( Q )
( c . ) P is more brittle than ( Q )
Deng’s modulus of than that of
11
375A river ( 10 m ) deep is flowing at ( 5 m / s )
The shearing stress between horizontal layers of the river is ( (boldsymbol{eta}= )
( 10^{-3} ) SI units
( mathbf{A} cdot 10^{-3} N / m^{2} )
B. ( 0.8 times 10^{-3} N / m^{2} )
C. ( 0.5 times 10^{-3} N / m^{2} )
D. ( 1 mathrm{N} / mathrm{m}^{2} )
11
376If a rubber ball is taken down to a ( 100 mathrm{m} ) deep lake, its volume decreases by ( 0.1 % )
If ( boldsymbol{g}=mathbf{1 0} quad boldsymbol{m} / boldsymbol{s}^{2} ) then the bulk modulus
of elasticity for rubber, in ( mathrm{N} / mathrm{m}^{2} ), is
A ( cdot 10^{8} )
B . ( 10^{text {9 }} )
c. ( 10^{11} )
D. ( 10^{10} )
11
377What is the tension in string B?
A. ( frac{3 m g}{5} )
в. ( frac{m g}{5} )
c. ( frac{6 m g}{5} )
D. ( frac{4 m g}{5} )
11
378The length of a metal is ( l_{1} ) when the
tension in it is ( T_{1} ) and is ( l_{2} ) when the
tension is ( T_{2} . ) The original length of the wire is :
A ( cdot frac{l_{1}+l_{2}}{2} )
в. ( frac{l_{1} T_{2}+l_{2} T_{1}}{T_{1}+T_{2}} )
c. ( frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} )
D. ( sqrt{T_{1} T_{2} l_{1} l_{2}} )
11
379When the load on a wire is increasing slowly from 2 kg to 4 kg, the elongation increases from ( 0.6 mathrm{mm} ) to ( 1 mathrm{mm} ). The
work done during this extension of the
wire is ( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) )
B . ( 0.4 times 10^{-3} ) J
c. ( 8 times 10^{-2} ) j
D. ( 10^{-3} ) 」
11
380The average depth of Indian ocean
is about 3000 m. The value of fractional
compression ( frac{Delta V}{V} ) of water at the
bottom of the ocean is:
[Given that the bulk modulus of water
is ( 2.2 times 10^{9} N m^{-2}, g=9.8 m s^{-2} ) and
( left.rho_{H_{2}} O=1000 k g . m^{-3}right] )
A. ( 3.4 times 10^{-2} )
B . ( 1.34 times 10^{-2} )
c. ( 4.13 times 10^{-2} )
D. ( 13.4 times 10^{-2} )
11
381A uniform rod of length ( L ) has a mass
per unit length ( lambda ) and area of cross
section ( A ). If the Young’s modulus of the
rod is ( Y . ) The elongation in the rod due to its own weight is
A ( cdot frac{2 lambda g L^{2}}{A Y} )
B. ( frac{lambda g L^{2}}{2 A Y} )
c. ( frac{lambda g L^{2}}{4 A Y} )
D. ( frac{lambda g L^{2}}{6 A Y} )
11
382Which of the following is an example of elastic deformation?
A. stretching a rubber band
B. stretching saltwater taffy
( c . ) both
D. none
11
383Out of the following whose elasticity is independent of temperature
A. stee
B. copper
c. Invar steel
D. glass
11
384Stress and pressure have the same
dimensions but pressure is not the same as stress.Why?
11
385Assertion (A) : Lead is more elastic than
rubber.

Reason (R) : If the same load is attached
to lead and rubber wires of the same
cross-sectional area, the strain of lead
is very much less than that of rubber.
A. Both assertion and reason are true and the reason is correct explanation of the assertion
B. Both assertion and reason are true, but reason is not correct explanation of the assertion
c. Assertion is true, but the reason is false
D. Assertion is false, but the reason is true

11
386Assertion
Ratio of isothermal bulk modulus and
adiabatic bulk modulus for a
monoatomic gas at a glven pressure is ( frac{3}{5} )
Reason This ratio is equal to ( gamma=frac{C_{p}}{C_{v}} )
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
387In figure the upper wire is made of steel
and the lower of copper. The wires have equal cross section. Find the ratio of the
ongitudinal strains developed in the
two wires.
11
388A copper rod of length ( L ) and radius ( r ) is suspended from the ceiling by one of its ends. What will be elongation of the rod due to its own weight when ( rho ) and ( Y ) are
the density and Young’s modulus of the copper respectively?
( ^{text {A } cdot frac{rho^{2} g L^{2}}{2 Y}} )
( ^{mathrm{B}} cdot frac{rho g L^{2}}{2 Y} )
c. ( frac{rho^{2} g^{2} L^{2}}{2 Y} )
D. ( frac{rho g L}{2 Y} )
11
389Take, bulk modulus of water ( boldsymbol{B}= )
( mathbf{2 1 0 0} boldsymbol{M P a} )
What increase in pressure is required to decrease the volume of 200 litres of
water by 0.004 percent?
A ( .210 k P a )
в. ( 840 mathrm{kPa} )
c. ( 8400 k P a )
D. ( 84 k P a )
11
390Which of the following are correct?
This question has multiple correct options
A. The shear modulus of a liquid is infinite.
B. Bulk modulus of a perfectly rigid body is infinity.
C. According to Hookes law, the ratio of the stress and strain remains constant.
D. None of the above.
11
391A steel ring of radius ( r ) and cross
sectional area ( A ) is fitted onto a wooden
disc of radius ( R(R>r) . ) If the Young’s
modulus of steel is ( Y ), then the force
with which the steel ring is expanded is
A. ( A Y(R / r) )
в. ( A Y(R-r) / r )
c. ( (Y / A)[(R-r) / r] )
D. ( Y r / A R )
11
392For a material ( Y=6.6 times 10^{10} mathrm{N} / mathrm{m}^{2} ) and
bulk modulus ( mathrm{K}=11 times 10^{10} mathrm{N} / mathrm{m}^{2}, ) then its
Poissons’s ratio is
A. 0.8
B. 0.35
( c . ) о.
D. 0.4
11
393A rubber cord of density d, Youngs modulus Y and length L is suspended vertically. If the cord extends by a length ( 0.5 mathrm{L} ) under its own weight, then Lis
A ( cdot frac{Y}{2 d g} )
в. ( frac{Y}{d g} )
c. ( frac{2 Y}{d g} )
D. ( frac{d g}{2 Y} )
E ( cdot frac{d g}{Y} )
11
394( boldsymbol{Y}, boldsymbol{k}, boldsymbol{n} ) represent respectively the
young’s modulus,bulk modulus and rigidity modulus of a body. If rigidity modulus is twice the bulk
modulus, then:
A. ( Y=5 k / 18 )
в. ( Y=5 n / 9 )
c. ( Y=9 k / 5 )
D. ( Y=18 k / 5 )
11
395A solid sphere hung at the lower end of a wire is suspended from a fixed point so
as to give an elongation of ( 0.4 m m ) When the first solid sphere is replaced by another one made of same material
but twice the radius, the new
elongation is
A . ( 0.8 m m )
в. ( 1.6 m m )
( mathrm{c} .3 .2 mathrm{mm} )
D. ( 1.2 m m )
11
396The volume of oil contained in a certain
hydraulic press is ( 0.2 m^{3} . ) The
compressibility of oil is ( 20 times 10^{-6} ) per
atmosphere. The decrease in volume of the oil when subjected to 200
atmospheres is (1 atmosphere ( = )
( left.1.02 times 10^{5} N / m^{2}right) )
A ( cdot 4 times 10^{-4} m^{3} )
B. ( 8 times 10^{-4} m^{3} )
c. ( 16 times 10^{-4} m^{3} )
D. ( 2 times 10^{-4} m^{3} )
11
397The bulk modulus of an ideal gas at
constant temperature is :
A. Equal to its pressure
B. Equal to its volume
c. Equal to ( p / 2 )
D. Cannot be determined
11
398Define the terms
(a) Plastic
(b) Adhesive
11
399A cubical ball is taken to a depth of ( 200 mathrm{m} ) in a sea. The decrease in volume
observed to be ( 0.1 % ). The bulk modulus of
the ball is ( left(10=m s^{-2}right) )
( begin{array}{ll}text { A. } 2 times 10^{7} & text { Pa } \ aend{array} )
В. ( 2 times 10^{6} ) Ра
C ( .2 .1 times 10^{9} ) Pa
D. ( 1.2 times 10^{9} ) Pa
11
400A metallic ring of radius ‘r’, cross sectional area ‘A’ is fitted into a wooden
circular disk of radius ‘R’ ( (R>r) . ) If the
Young’s modulus of the material of the ring is ‘Y’, the force with which the metal ring expands is :
A. ( frac{A Y R}{r} )
в. ( frac{A Y(R-r)}{r} )
c. ( frac{Y(R-r)}{A r} )
D. ( frac{Y R}{A r} )
11
401A steel rope has length ( L ), area of cross-
section ( A ), Young’s modulus ( Y ). Density ( =d ) ]. If the steel rope is
vertical and moving with the force acting vertically up at the upper end, find the strain at a point ( frac{L}{3} ) from lower
end.
( mathbf{A} cdot(d g L) / 2 Y )
в. ( (d g L) / 4 Y )
( mathbf{c} cdot(d g L) / 6 Y )
D. ( (d g L) / 8 Y )
11
402Which of the following statements is
true for wave motion?
A. Mechanical transverse wave can propagate through all medium.
B. Longitudinal waves can propagate through solids only.
C. Mechanical transverse waves can propagate through solids only.
D. Longitudinal waves can propagate through vacuum.
11
403The pressure applied from all directions
on a cube is ( p . ) How much its
temperatures should be raised to maintain the original volume? The
volume elasticity of the cube is ( beta ) and
the coefficient of volume expansion is ( alpha )
A ( cdot frac{p}{alpha beta} )
B. ( frac{p alpha}{beta} )
( c cdot frac{p beta}{alpha} )
D. ( frac{alpha beta}{p} )
11
404In a sphere, that is fully submerged in a İiquid,
A. Force is applied along one of the diameter to determine the volume stress
B. Force is applied along two perpendicular diameters to determine the volume stress
C. Force is applied along the entire surface to determine the volume stress
D. Force is applied along the hemispherical surface to determine the volume stress
11
405If Young’s modulus of iron be ( 2 times 10^{11} )
( mathrm{N} / mathrm{m}^{-2} ) and interatomic distance be ( 3 mathrm{x} )
( 10^{-10} mathrm{m}, ) the interatomic force constant
will be :
( mathbf{A} .60 N / m )
в. ( 120 N / m )
( c .30 N / m )
D. ( 180 N / m )
11
406The Poissons ratio for inert gases is:
A . 1.40
B . 1.66
( c cdot 1.34 )
D. None of these
11
407The mean distance between the atoms
of iron is ( 3 times 10^{-10} m ) and interatomic
force constant for iron is ( mathbf{7} N boldsymbol{m}^{-1} ). The
Young’s modulus of electricity for iron
is
A ( .2 .33 times 10^{5} mathrm{Nm}^{-2} )
в. ( 23.3 times 10^{10} mathrm{Nm}^{-2} )
c. ( 2.33 times 10^{9} mathrm{Nm}^{-2} )
D. ( 2.33 times 10^{10} mathrm{Nm}^{-2} )
11
408following graphs correctly represents
the variation of extension in the length
of a wire with the external load?
( A )
B.
( c )
D.
11
409The formula ( Y=3 B(1-2 sigma) ) relates
young’s modulus and bulk’s modulus with poisson’s ratio. A theoretical physicist derives this formula incorrectly as ( Y=3 B(1-4 sigma) )
According to this formula, what would be the theoretical limits of poisson’s
ratio:
A. Poisson’s ratio should be less than 1
B. Poisson’s ratio should be less than 0.5
c. Poisson’s ratio should be less than 0.25
D. Poisson’s ratio should be less than 0
11
410Which of the following relation is true?
A. ( 3 Y=K(1+sigma) )
в. ( _{K}=frac{9 eta Y}{Y+eta} )
( mathbf{c} cdot sigma=(6 K+eta) Y )
D. ( sigma=frac{0.5 Y-eta}{eta} )
11
411For most materials, the Young’s
modulus is ( n ) times the modulus of
rigidity, where ( n ) is
( A cdot 2 )
B. 3
( c cdot 4 )
D. 5
11
412If a member, whose tensile strength is more than 1.5 times the shear strength and is subjected to an axial load upto failure, the failure of the member will
occur by
A. maximum normal stress
B. maximum shear stress
c. normal stress or shear stress
D. none of the above
11
413The Poisson’s ratio of a material is ( 0.5 . ) If
a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4%. The percentage increase in the length is :
A . 1%
B. २%
c. 2.5%
D. 4%
11
414A wire elongates by 1 m ( m ) when a load
( W ) is hung from it. If the wire goes over
a pulley and the two weights ( W ), each are hung at the two ends, then the elongation of the wire will be:
A. ( 0.5 m m )
в. ( 1 mathrm{mm} )
( mathbf{c} cdot 2 m m )
D. ( 4 m m )
11
415The elastic relaxation time is minimum
for
A. glass
B. quartz
c. rubber
D. clay
11
416A fixed volume of iron is drawn into a
wire of length ( L ). The extension ( x ) produced in the wire by a constant force
( F . F ) is proportional to
A ( cdot frac{1}{L^{2}} )
в. ( frac{1}{L} )
c. ( L^{2} )
D. ( L )
11
417The length of an elastic string is ( L_{1} )
when the tension is ( 4 N, ) and ( L_{2} ) when
the tension is 5 N. What is the length of
the string when the tension is ( 7 N ? )
11
418The unit of stress is:
A . ( k g m^{-2} )
B. ( N k g^{-1} )
c. ( N m^{-2} )
D. ( N )
11
419When the tension in a metal wire is ( T_{1} )
its length is ( l_{1} ). When the tension is ( T_{2} )
its length is ( l_{2} ). The natural length of
wire is
( ^{mathbf{A}} cdot frac{T_{2}}{T_{1}}left(l_{1}+l_{2}right) )
в. ( T_{1} l_{1}+i_{2} l_{2} )
c. ( frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} )
D. ( frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}} )
11
420A sphere contracts in volume by ( 0.01 % ) when taken to the bottom of sea ( 1 mathrm{km} ) deep. Find bulk modulus of the material
of sphere
A. ( 9.8 times 10^{6} M / M^{2} )
В. ( 1.2 times 10^{10} N / M^{2} )
c. ( 9.8 times 10^{10} N / M^{2} )
D. ( 9.8 times 10^{11} N / M^{2} )
11
421Find the density of lattice, A compound
AB has a rock type structure with ( A: B= )
1 : 1. The formula mass of AB is 6.023 Y
amu and the closed ( A ) -B distance is
( boldsymbol{Y}^{1 / 3} mathrm{nm} )
A ( cdot 4 mathrm{kg} / m^{3} )
в. ( 5 mathrm{kg} / mathrm{m}^{3} )
c. ( 40 mathrm{kg} / mathrm{m}^{3} )
D. ( 50 mathrm{kg} / mathrm{m}^{3} )
11
422Two vertical rods of equal lengths, one of steel and the other of copper, are
suspended from the ceiling, at a distance I apart and are connected
rigidly to a rigid horizontal bar at their
lower ends. If ( A_{S} ) and ( A_{C} ) be their
respective cross-sectional areas, and
( boldsymbol{Y}_{boldsymbol{S}} ) and ( boldsymbol{Y}_{C}, ) their respective Young’s
moduli of elasticities, where should a
vertical force ( F ) be applied to the horizontal bar in order that the bar
remains horizontal?
11
423A copper rod of length ( l ) is suspended from the ceiling by one of its ends. Find the relative increment of its volume
( frac{Delta V}{V} )
A ( cdot frac{Delta V}{V}=(1-2 mu) frac{Delta l}{l} )
в. ( frac{Delta V}{V}=(1-3 mu) frac{Delta l}{l} )
c. ( frac{Delta V}{V}=(1-2 mu) frac{2 Delta l}{l} )
D. ( frac{Delta V}{V}=(1-3 mu) frac{3 Delta l}{l} )
11
424A load of ( 10 k N ) is supported from a
pulley which in turn is supported by a rope of sectional area, ( 1 times 10^{3} m m^{2} )
and modulus of elasticity ( 10^{3} N m m^{-2} ) as shown in Fig. 5.18. Neglecting the friction at the pulley, determine the deflection of the load is ( x+0.75 m m )
Find ( boldsymbol{x} )
11
425A bar of cross-sectional area ( boldsymbol{A} ) is
subjected two equal and opposite tensile forces at its ends as shown in
figure. Consider a plane BB’ making an
angle ( theta ) with the length.
The ratio of tensile stress to the
shearing stress on the plane BB’ is:
( A cdot tan theta )
B. ( sec theta )
( c cdot cot theta )
( D cdot cos theta )
11
426A steel wire is suspended from a fixed end, while the other end is loaded with a
weight W. This produced an extension ( x ) As the weight is increased, the extension was also increased. A plot of
extension vs load within elastic limits
will give rise to
A. a curve
B. an ellipse
c. a straight line
D. a hyperbola
11
427( mathbf{A} )
( 2 m ) long rod of radius ( 1 c m ) which is
fixed from one end is given a twist of 0.8 radian. The shear strain developed will
be
( mathbf{A} cdot 0.002 )
B. 0.004
c. 0.008
D. 0.016
11
428The ratio of lateral strain to the linear
strain within elastic limit is known as:
A. Young’s modulus
B. Bulk’s modulus
c. Rigidity modulus
D. Poisson’s ratio
11
429The length of a wire is increased by
1 ( m m ) on the application of a given load In a wire of the same material, but of length and radius twice that of the first, on application of the same load, extension is
A. ( 0.25 mathrm{mm} )
в. ( 0.5 mathrm{mm} )
( mathrm{c} .2 mathrm{mm} )
D. ( 4 mathrm{mm} )
11
430A steel rod has a radius of ( 10 mathrm{mm} ) and a
length of ( 1.0 mathrm{m} . ) A force stretches it along its length and produces a strain of ( 0.16 % . ) Young’s modulus of the steel is ( 2.0 times 10^{11} N / m^{2} . ) What is the
magnitude of the force stretching the rod?
A . ( 100 mathrm{kN} )
B. 314 k
c. ( 31.4 mathrm{kN} )
D. 200kN
11
431When a ( 4 k g ) mass is hung vertically on a light spring that obeys Hooke’s law,
the spring stretches by 2 cms. The work required to be done by an external agent in stretching this spring by ( 5 c m s ) will
be ( left(boldsymbol{g}=mathbf{9 . 8 m} / boldsymbol{s e c}^{2}right) )
A. 4.900 joule
B . 2.450 joule
c. 0.495 joule
D. 0.245 joule
11
432A steel wire of length ( 5 mathrm{m} ) is pulled to have an extension of ( 1 mathrm{mm} ). Its ( mathrm{Y} ) is ( 1.9 mathrm{x} )
( 10^{4} mathrm{N} / mathrm{m}^{2} . ) The energy per unit volume stored in it is
A ( .3 .8 times 10^{-4} mathrm{J} / mathrm{m}^{3} )
B . ( 7.6 times 10^{-4} J / m^{3} )
C ( .1 .9 times 10^{-4} J / m^{3} )
D. ( 0.95 times 10^{-4} mathrm{J} / mathrm{m}^{3} )
11
433To what depth must a rubber ball be taken in deep sea so that its volume is
decreased by ( 0.1 % ) (Take density of sea water ( 10^{3} k g quad m^{-3} )
bulk modulus of rubber ( =9 times )
( mathbf{1 0}^{8} mathbf{N m}^{-mathbf{2}}, boldsymbol{g}=mathbf{1 0 m} boldsymbol{s}^{-mathbf{2}} mathbf{)} )
( A .9 m )
в. 18 т
( mathrm{c} .90 mathrm{m} )
D. ( 180 m )
11
434Which of the following statement
related to stress-strain relation is
correct?
A. Stress is linearly proportional to strain irrespective of the magnitude of the strain
B. Stress is linearly proportional to strain above
C. Stress is linearly proportional to strain for stress much smaller than at the yield point
D. Stress-strain curve is same for all materials
E. Stress is inversely proportional to strain
11
435A wire made of the material of Young’s modulus ( Y ) has an stress ( S ) applied to
it. If Poisson’s ratio of the wire is ( sigma ), the
lateral strain is:
( ^{text {A }} cdot frac{S}{Y} )
в. ( sigma frac{Y}{S} )
c. ( sigma Y times S )
D. ( frac{s}{sigma Y} )
11
436The bulk modulus of water is ( 2.1 times )
( 10^{9} N / m^{2} . ) The pressure required to
increase the density of water by ( 0.1 % )
is:-
A ( cdot 2.1 times 10^{5} N / m^{2} )
B . ( 2.1 times 10^{3} N / m^{2} )
C ( cdot 2.1 times 10^{6} N / m^{2} )
D. ( 2.1 times 10^{7} N / m^{2} )
11
437Stressis a ( -ldots— ) quantity.
A. scalar
B. vector
c. tensor
D. dimensionless
11
438The ratio of modulus of rigidity to modulus of elasticity for a Poisson’s ratio of 0.25 would be
A. 0.5
B. 0.4
( c cdot 0.3 )
D. 1.0
11
439Strain energy per unit volume in a stretched string is
A. ( 1 / 2 times ) Stress ( times ) Strain
B. Stress x Strain
c. (Stress x Strain) ( ^{2} )
D. Stress / Strain
11
440For a material ( sigma=-0.25 ) under an
external stress, the longitudinal strain
is ( 10^{-2} ). The percentage change in the diameter of the wire is
A . ( +1 % )
B. -1%
c. ( +0.25 % )
D. – 0.25%
11
441Which of the following is not artificial form of plastics?
A. Nylon
B. Teflon
c. Styrofoam
D. None of the above
11
442For a given material, the Young’s modulus is 2.4 times that of rigidity modulus. Its poisson’s ratio is.
A . 2.4
B. 1.2
( c .0 .4 )
D. 0.2
11
443A material capable of absorbing large amount of energy before fracture is
known as
A. Ductility
B. Toughness
c. Resilience
D. Plasticity
11
444One end of a horizongal thick copper wire of length ( 2 L ) and radius ( 2 R ) is welded to an end of another horizontal
thin copper wire of length ( L ) and radius
( R ) When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is then
A . 0.25
B. 0.50
( c .2 .00 )
D. 4.00
11
445Which of the following pairs is not
correct?
A. strain-dimensionless
B. stress-N/m ( ^{2} )
c. modulus of elasticity- ( N / m^{2} )
D. poisson’s ratio- ( N / m^{2} )
11
446If speed(V), acceleration(A) and force(F) are considered as fundamental units,
the dimension of Young’s modulus will
be?
A. ( V^{-2} A^{2} F^{2} )
a ( cdot F^{-2} F^{-} )
В. ( V^{-4} A^{2} F )
c. ( V^{-4} A^{-2} F )
D. ( V^{-2} A^{2} F^{-2} )
11
447Assertion
Yield strength is the stress required to produce a small specific amount of deformation.
Reason
The offset yield strength can be
determined by the stress corresponding
to the intersection of the stress-strain
curve and a line parallel to the elastic line offset by a strain of 0.2 or ( 0.1 % )
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
448A wire of length ( L ) and cross-sectional ( A )
is made of a material of Young’s
modulus. If the wire is stretched by an amount ( x, ) the work done is
11
449One end of a nylon rope of length ( 4.5 m )
and diameter ( 6 m m ) is fixed to a stem of
a tree. A monkey weighting ( 100 N ) jumps to catch the free end and stays there. what will be the change in the diameter of the rope. (Given Young’s modulus of nylon ( =4.8 times 10^{11} N m^{-2} )
and Poisson’s ratio of nylon ( =0.2 ) )
A. ( 8.8 times 10^{-9} mathrm{m} )
в. ( 7.4 times 10^{-9} mathrm{m} )
c. ( 6.4 times 10^{-8} mathrm{m} )
D. ( 5.6 times 10^{-9} mathrm{m} )
11
450The Poisson’s ratio of a material is ( 0.8 . ) If
a force is applied to a wire of this material decreases its cross-sectional
area by ( 4 %, ) then the percentage increase in its length will be.
A . ( 1 % )
B. 2%
( c .2 .5 % )
D. ( 4 % )
11
451Figure shows the strain-stress curve for
a given material. The Young’s modulus
of the material is
( mathbf{A} cdot 5 times 10^{9} N quad m^{-2} )
B . ( 5 times 10^{10} N quad m^{-2} )
( begin{array}{lll}text { С. } 7.5 times 10^{9} N & m^{-2}end{array} )
D. ( 7.5 times 10^{10} N quad m^{-2} )
11
452Find the depth of a lake at which
density of water is ( 1 % ) greater than at
the surface. Given compressibility ( K= ) ( 50 times 10^{-6} / ) atm
11
453The property of metals which allows them to be drawn readily into thin wires is:
A. elasticity
B. ductility
c. hardness
D. malleability
11
454One end of a steel rectangular girder is embedded into a wall (figure shown above). Due to gravity it sags slightly. Find the radius of curvature of the
neutral layer (see the dotted line in the figure above) in the vicinity of the point
( O ) if the length of the protruding section
of the girder is equal to ( l=6.0 m ) and
the thickness of the girder equals ( h= )
( 10 mathrm{cm} )
11
455The fractional increase in volume of a
wire of circular cross section, if its lingitudinal strain is ( 1 %(sigma=0.3) )
A . 0.4
B. 0.04
c. 0.004
D. 4
11
456Q Type your question
steel, a student can record the
following values:
length of wire ( mathrm{I}=left(ell_{0} pm Delta mathrm{I}right) boldsymbol{m} )
diameter of wire ( boldsymbol{d}=left(boldsymbol{d}_{0} pm boldsymbol{Delta} boldsymbol{d}right) mathrm{mm} )
force applied to wire ( boldsymbol{F}=left(boldsymbol{F}_{0} pm boldsymbol{Delta} boldsymbol{F}right) boldsymbol{N} )
extension of wire ( e=left(e_{0} neq Delta eright) mathrm{mm} )
In order to obtain more reliable value for
( Y, ) the following three techniques are
suggested

Technique (i) A shorter wire Is to be used.
Technique
(ii) The diameter shall be
measured at several places with a
micrometer screw gauge. Technique (iii) Two wires are made irom the same ntaterial and of same length. One is loaded at a fixed weight and acts as a reference for the extension of the
other which is load- tested Which of the above techniques is/are useful?
A. i and ii only
B. ii and iii only
c. i only
D. iii only

11
457An aluminium wire and steel wire of the
same length and cross section are
joined end to end.The composite wire is hung from a rigid support and a load is suspended from the free end.

The young’s modulus of steel is ( 20 / 7 ) times the aluminium. The ratio of
increase of length of steel and aluminium is
A ( .20 / 7 )
в. ( 400 / 49 )
( c cdot 7 / 20 )
D. ( 49 / 400 )

11
458The temperature of a wire is doubled. The Young’s modulus of elasticity will?
A. also double
B. become four times
c. remain same
D. decrease
11
459The graph shows the behaviour of a
steel wire in the region for which the wire obeys Hooke’s law.The graph is a part of a parabola. The variables x and y might represent
A. ( x= ) stress ( ; y= ) strain
B. ( x= ) strain ; ( y=operatorname{str} e s )
c. ( x= ) strain ( ; y= ) elastic energy
D. ( x= ) elastic energy ( ; y= ) strain
11
460A sphere contracts in volume by ( 0.01 % ) when taken to the bottom of lake ( 1 k m )
deep. If the density of water is ( 1 g m / c c )
the bulk modulus of water is
A ( cdot 9.8 times 10^{5} mathrm{N} / mathrm{m}^{2} )
B. ( 9.8 times 10^{8} mathrm{N} / mathrm{m}^{2} )
c. ( 9.8 times 10^{10} mathrm{N} / mathrm{m}^{2} )
D. 9.8 ( times 10^{6} mathrm{N} / mathrm{m}^{2} )
11
461A uniform rod of length ( L ) and density ( rho )
is being pulled along a smooth floor with a horizontal acceleration ( a ). Find
the magnitude of the stress at the transverse cross section through the mid-point of the rod.
11
462When the load on a wire is increased
from ( 3 k g w t ) to ( 5 k g w t ) the elongation increases from 0.61 ( m m ) to ( 1.02 m m )
The required work done during the extension of the wire is:
A ( cdot 16 times 10^{-3} J )
В. ( 8 times 10^{-2} J )
c. ( 20 times 10^{-2} J )
D. ( 11 times 10^{-3} J )
11
463Choose the correct statements from the
following:
This question has multiple correct options
A. Steel is more elestic than rubber
B. Fluids have Youngs modulus as well as shear modulus
C. Solids have Youngs modulus, bulk modulus as well as shear modulus
D. Bulk modulus of water is greater than that of copper.
11
464A rubber cord of length ( 40 mathrm{cm} ) and area
of cross section ( 4 times 10^{-6} mathrm{m}^{2} ) is extended
by 10cm. If the energy gained is 20 joule young’s modulus of rubber is
( mathbf{A} cdot 10^{8} N m^{-2} )
B . ( 2 times 10^{8} mathrm{Nm}^{-2} )
( mathbf{c} cdot 4 times 10^{8} mathrm{Nm}^{-2} )
D. ( 1.5 times 10^{6} N m^{-2} )
11
465Longitudinal strain is calculated using the formula
A. Change in length/ original length
B. original length/change in length
c. original length ( times ) change in length
D. original length – change in length
11
466Two wires of the same material and
length are stretched by the same force. Their masses are in the ratio ( 3: 2 . ) Their
elongations are in the ratio
A .3: 2
B. 9: 4
c. 2: 3
D. 4: 9
11
467What do you mean by elastic bodies and plastic.11
468When a weight ( mathrm{W} ) is hung from one end of a wire of length ( L ) (other end being fixed), the length of the wire increases by 1. If the same wire is passed over a pulley and two weights Weach are hung at the two ends, what will be the total
elongation in the wire?
11
469Which of the following deformations is/are irreversible?
This question has multiple correct options
A. Elastic deformation
B. Plastic deformation
c. Fracture
D. All of the above
11
470Two different types of rubber are found
to have the stress-strain curve as
shown. Then
A. ( A ) is suitable for shock absorber
B. ( B ) is suitable for shock absorber
( mathrm{c} . B ) is suitable for car types
D. None of these
11
471State whether true or false:
The metal used in construction of a
bridge should have high Young’s modulus.
A. True
B. False
11
472A wire is subjected to a tensile stress. If
A represents area of cross-section,
represents original length, I represents extension and Y is Young’s modulus of elasticity, then elastic potential energy of the stretched wire is
( mathbf{A} cdot U=frac{2 L}{A Y} I^{2} )
B ( cdot U=frac{A L}{2 Y} I^{2} )
( mathbf{c} cdot U=frac{A Y}{2 L} I^{2} )
D. ( U=frac{1}{4} frac{A Y}{L} I^{2} )
11
473A mild steel wire of length ( 1.0 mathrm{m} ) and
cross-sectional area ( 0.50 times 10^{-2} mathrm{cm}^{2} )
is stretched, well within its elastic
limit, horizontally between two pillars. A mass of ( 100 mathrm{g} ) is suspended from the mid-point of the wire. Calculate the depression at the mid-point.
11
474The Young’s modulus of a wire of length
( boldsymbol{L} ) and radius ( boldsymbol{r} ) is ( boldsymbol{Y} boldsymbol{N} / boldsymbol{m}^{2} . ) The length
and radius are reduced to ( frac{L}{6} ) and ( frac{r}{6} ) then its Young’s modulus is :
( A cdot 6 Y )
в. ( frac{Y}{6} )
( c cdot Y )
D. ( 3 Y )
11
475When a metal wire is stretched by a load, the fractional change in its volume ( Delta V / V ) is proportional to?
( ^{mathrm{A}} cdot-frac{Delta l}{l} )
( ^{mathrm{B}}left(frac{Delta l}{l}right)^{2} )
c. ( sqrt{Delta l / l} )
D. None of these
11
476Let L be the length and d be the
diameter of cross-section of a wire.
Wires of the same material with
different L and d are subjected to the same tension along the length of the wire. In which of the following cases, the extension of wire will be the maximum?
A. ( L=200 mathrm{cm}, d=0.5 mathrm{mm} )
в. ( L=300 mathrm{cm}, d=1.0 mathrm{mm} )
c. ( L=50 mathrm{cm}, d=0.05 mathrm{mm} )
D. ( L=100 mathrm{cm}, d=0.2 mathrm{mm} )
11
477Identical springs of steel and copper
( left(boldsymbol{Y}_{text {steel}}>boldsymbol{Y}_{text {copper}}right) ) are equally stretched
then:
A. Less work is done on copper spring
B. Less work is done on steel spring
c. Equal work is done on both the springs
D. Data is incomplete
11
478A wire of uniform cross section is hanging vertically and due to its own weight its length changes. There is a point ‘C’ on the wire such that change in length AC is equal to the change in length BC. Points ( A, B ) and ( C ) are shown in the figure. Find ( frac{boldsymbol{A C}}{boldsymbol{B C}} )
A ( cdot sqrt{2}-1 )
B. ( frac{sqrt{2}-1}{sqrt{2}+1} )
c. ( frac{sqrt{2}+1}{sqrt{2}-1} )
D. None of these
11
479A steel rod of length ( I, ) area of cross
section ( A, ) Young’s modulus ( E ) and linear
coefficient of expansion a is heated through ( t^{circ} C . ) The work that can be
performed by the rod when heated is
A ( cdot(E A a t) times(l a t) )
B ( cdot frac{1}{2}(E A a t) times(l a t) )
c. ( frac{1}{2}(E A a t) times frac{1}{2}(l a t) )
D. 2(EAat)(lat)
11
480If ‘S’ is stress and ‘Y’ is Young’s modulus of a wire material, then energy stored in the wire per unit volume, is?
A ( cdot frac{s^{2}}{2 Y} )
в. ( frac{2 Y}{S^{2}} )
c. ( frac{s}{2 Y} )
( mathbf{D} cdot 2 S^{2} Y )
11
481In the Searle’s method to determine the
Young’s modulus of a wire, a steel wire of length ( 156 c m ) and diameter
( 0.054 mathrm{cm} ) is taken as experimental wire the average increase in length for 1.5 ( k g w t ) is found to be ( 0.050 c m ). then
the Ypung’s modulus of the wire is
A ( .3 .002 times 10^{11} N / m^{2} )
В. ( 1.002 times 10^{11} N / m^{2} )
c. ( 2.002 times 10^{11} N / m^{2} )
D. ( 2.5 times 10^{11} N / m^{2} )
11
482A block of weight ( 100 mathrm{N} ) is suspended by copper and steel wires of same cross
sectional area ( 0.5 mathrm{cm}^{2} ) and, length ( sqrt{3} m )
and ( 1 m, ) respectively. Their other ends
are fixed on a ceiling as shown in figure. The angles subtended by copper and
steel wires with ceiling are ( 30^{circ} ) and ( 60^{circ} ) respectively. If elongation in copper wire
is ( left(Delta l_{C}right) ) and elongation in steel wire is
( left(Delta l_{S}right), ) then the ratio ( frac{Delta l_{C}}{Delta l_{S}} ) is
(Young’s modulus for copper and steel
( operatorname{are} 1 times 10^{11} N / m^{2} ) and ( 2 times 10^{11} N / m^{2} )
respectively)
11
483Assuming that shear stress at the base of a mountain is equal to the force per
unit area due to its weight. Calculate the maximum possible height of a mountain on the earth if breaking stress of a typical rock is ( 3 times 10^{8} N m^{-2} )
and its density is then ( 3 times 10^{3} k g quad m^{-3} )
(Take ( left.g=10 m s^{-2}right) )
( A .4 k m )
в. ( 8 k m )
c. ( 10 k m )
D. ( 16 k m )
11
484Define Poisson’s ratio.11
485Assertion (A): Stress is restoring force per unit area.

Reason (R) : Interatomic forces in solids
are responsible for the property of
elasticity
A. Both Assertion and Reason are true and the reason is correct explanation of the assertion
B. Both Assertion and Reason are true, but reason is not correct explanation of the assertion
c. Assertion is true, but the Reason is false
D. Assertion is false, but the reason is true

11
486Which one of the following is not a unit of Young’s modulus?
( mathbf{A} cdot N m^{-1} )
B. ( N m^{-2} )
c. mega pascal
D. dyne ( c m^{-2} )
11
487One end of a uniform bar of weight ( boldsymbol{w}_{1} ) is suspended from the roof and a weight
( boldsymbol{w}_{2} ) is suspended from the other end, the area of cross-section is A. What is the
stress at the mid point of the rod?
A. ( frac{w_{1}+w_{2}}{A} )
в. ( frac{w_{1}-w_{2}}{A} )
c. ( frac{left(w_{1} / 2right)+w_{2}}{A} )
D. ( frac{w_{2} / 2+w_{1}}{A} )
11
488When a uniform wire of radius r is
stretched by a ( 2 k g ) weight, the increase
in its length is 2.00 mm. If the radius of
the wire is ( r / 2 ) and other conditions
remain in the same, increase in
its length is
A. ( 2.00 mathrm{mm} )
в. ( 4.00 mathrm{mm} )
c. ( 6.00 m m )
D. ( 8.00 m m )
11
489A 6 -kg weight is fastened to the end of a steel wire of un-stretched length ( 60 mathrm{cm} )
It is whirled in a vertical circle and has
an angular velocity of 2 revolution per second at the bottom of the circle. The
area of cross-section of the wire is
( 0.05 c m^{2} . ) Calculate the elongation of the
wire when the weight is at the lowest point of the path. Young’s modulus of steel ( =2 times 10^{11} mathrm{Pa} )
11
490Assertion
Brittle materials do not exhibit an
identifiable yield point; rather, they fail by brittle fracture.
Reason
The value of the largest stress in tension and compression defines the ultimate strength.
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
491Two wires of equal length and cross-
sectional area are suspended as shown
in figure. Their Young’s modulii are ( Y_{1} )
and ( Y_{2} ) respectively. The equivalent
Young’s modulii will be:
A ( cdot Y_{1}+Y_{2} )
B.
c. ( frac{Y_{1}+Y_{2}}{2} )
D. ( sqrt{Y_{1} Y_{2}} )
11
492The amount of work done in increasing
the length of a wire through ( 1 mathrm{cm} ) will be
A. ( frac{Y A}{2 L} )
в. ( frac{Y L}{2 A} )
c. ( frac{Y L^{2}}{2 A} )
D. None of these
11
493State whether the following statements are true or false with reasons.
When a wire is loaded beyond the elastic limit and then deloaded. the
work done disappears completely as
heat
A. True
B. False
11
494The proportional limit of steel is ( 8 x ) ( 10^{8} N / m^{2} ) and its Young’s modulus is
( mathbf{2} times mathbf{1 0}^{11} mathbf{N} / mathbf{m}^{2} . ) The maximum
elongation, a one metre long steel wire can be given without exceeding the proportional limit is
( A cdot 2 m m )
B. ( 4 mathrm{mm} )
( mathrm{c} cdot 1 mathrm{mm} )
D. 8 mm
11
495Longitudinal strain is possible in
A. Liquid
B. Gases
c. Solid
D. All of these
11
496A copper wire and a steel wire of the
same length and same cross section are joined end to end to form a
composite wire. The composite wire is hung from a rigid support and a load is suspended from the other end. If the increase in length of the composite wire is 2.4 mm, then the increase in lengths
of steel and copper wires are:
( left(Y_{c u}=10 times 10^{10} N / m^{2}, Y_{s t e e l}=2 timesright. )
( left.10^{11} N / m^{2}right) )
( mathbf{A} cdot 1.2 m m, 1.2 m m )
в. ( 0.6 mathrm{mm}, 1.8 mathrm{mm} )
c. ( 0.8 m m, 1.6 m m )
D. ( 0.4 mathrm{mm}, 2.0 mathrm{mm} )
11
497The length of a metal wire is ( l_{1} ) when the tension in it is ( F_{1} ) and ( l_{2} ) when the
tension is ( F_{2} ). Then original length of the wire is:
A. ( frac{l_{1} F_{1}+l_{2} F_{2}}{F_{1}+F_{2}} )
в. ( frac{l_{2}-l_{1}}{F_{2}-F_{1}} )
c. ( frac{l_{1} F_{2}-l_{2} F_{1}}{F_{1}-F_{2}} )
D. ( frac{l_{1} F_{1}-l_{2} F_{2}}{F_{2}-F_{1}} )
11
498A vertical steel post of diameter ( 25 mathrm{cm} )
and length ( 2.5 m ) supports a weight of
( 8000 k g . ) Find the change in length
produced. (Given ( left.boldsymbol{Y}=mathbf{2} times mathbf{1 0}^{mathbf{1 1}} boldsymbol{P a}right) )
( A cdot 2.1 mathrm{cm} )
B. 0.21 ( mathrm{cm} )
c. ( 0.21 mathrm{mm} )
D. 0.021 mm
11
499Force vs Elongation graph of a wire is shown in the figure for two different
temperatures ( boldsymbol{T}_{1} & boldsymbol{T}_{2}, ) then
A ( cdot T_{1}=T_{2} )
В ( cdot T_{1}T_{2} )
D. cannot be predicted
11
500The stress required to double the length of wire (or) to produce ( 100 % ) Iongitudinal strain is:
A. ( Y )
в. ( frac{Y}{2} )
( c .2 Y )
D. ( 3 Y )
11
501A uniform cylindrical wire of length ( 4 m )
and diameter ( 0.6 m m ) is stretched by a
certain force such that its length is
increased by ( 4 m m . ) If the Poisson’s ratio
of the material is 0.3 then, calculate the
change in diameter of the wire.
11
502The length of two wires are in the ratio
( 3: 4 . ) Ratio of the diameters is 1: 2
young’s modulus of the wires are in the
ratio ( 3: 2 ; ) If they are subjected to same
tensile force, the ratio of the elongation produced is
A . 1:
B. 1: 2
c. 2: 3
( D cdot 2: )
11
503A brass rod has a length of ( 0.2 m, ) area of
cross section ( 1.0 mathrm{cm}^{2} ) and young’s
modulus ( 10^{11} mathrm{Nm}^{-2} . ) If it is compressed
by ( 5 k g ) weight along its length, then the change in its energy will be :
A. an increase of ( 2.4 times 10^{-5} ) j
B. a decrease of ( 2.4 times 10^{-5} mathrm{J} )
c. an increase of ( 2.4 times 10^{7} ) J
D. a decrease of ( 2.4 times 10^{7} ) j
11
504When a wire is subjected to a force along its length, its length increases by ( 0.4 % ) and its radius decreases by ( 0.2 % )
Then the Poisons ratio of the material of
the wire is
A . 0.8
B. 0.5
( c .0 .2 )
D. ( 0 . )
11
505Which one is more elastic steel or
rubber.Explain.
11
506Three bars having length ( l, 2 l ) and ( 3 l ) and area of cross-section ( A, 2 A ) and ( 3 A ) are
joined rigidly and to end. Compound rod is subjected to a stretching force ( boldsymbol{F} ). The increase in length of rod is (Young’s modulles of material is ( Y ) and bars are
massless)
A ( cdot frac{13 F l}{2 A Y} )
в. ( frac{3 F l}{A Y} )
c. ( frac{9 F l}{A Y} )
D. ( frac{13 mathrm{Fl}}{mathrm{AY}} )
11
507Region between elastic point and yield point is known as
A. Elastoplastic region
B. Electronegative region
c. Electro ductile region
D. Electro plating region
11
508A rubber cord catapult has cross-
sectional area ( 25 mathrm{mm}^{2} ) and initial
length of rubber cord is ( 10 mathrm{cm} . ) It is stretched to ( 5 mathrm{cm} ) and then released to
project a missile of mass 5 g. Taking ( boldsymbol{Y}_{r u b b e r}=mathbf{5} times mathbf{1 0}^{8} boldsymbol{N} boldsymbol{m}^{-2}, ) velocity of
projected missile is:
A. ( 20 mathrm{ms}^{-1} )
B. ( 100 mathrm{ms}^{wedge}(-1) $ $ )
c. ( 250 mathrm{ms}^{-1} )
D. ( 200 mathrm{ms}^{-1} )
11
509In materials like aluminium and
copper, the correct order of magnitude of various elastic moduli is
A. Young’s modulii < shear modulii < bulk modulii.
B. Bulk modulii < shear modulii <Young's modulii
c. shear modulii < Young's modulii < bulk modulii
D. Bulk modulii <Young's modulii < shear modulii
11
510A steel cable with a radius ( 2 c m )
supports a chairlift at a ski area. If the
maximum stress is not to exceed
( 10^{8} N quad m^{-2}, ) the maximum load the
cable can support is
A ( cdot 4 pi times 10^{5} N )
B ( cdot 4 pi times 10^{4} N )
C ( .2 pi times 10^{5} N )
D. ( 2 pi times 10^{4} N )
11
511A steel girder can bear a load of 20 tons. If the thickness of girder is double, then for the same depression it can bear a load of :
A. 40 ton
B. 80 ton
( c . ) 160 ton
( D cdot 5 ) ton
11
512The compressibility of water is ( 4 times 10^{-5} )
per unit atmosphere pressure. The
decrease in volume of ( 100 mathrm{cm}^{3} ) water
under a pressure of 100atm will be
A ( cdot 0.4 mathrm{cm}^{3} )
B. ( 4 times 10^{-5} mathrm{cm}^{3} )
c. ( 0.025 mathrm{cm}^{3} )
D. ( 0.04 mathrm{cm}^{3} )
11
513A spring of spring constant ( 5 times 10^{3} mathrm{Nm}^{-1} )
is stretched initially by ( 5 c m ) from the unstretched position. Then the work required to stretch it further by another
( 5 c m ) is
A. ( 6.25 N m )
B . ( 12.50 mathrm{Nm} )
c. ( 18.75 N m )
D. ( 25.00 N m )
11
514The diagram shows the stress v/s strain
curve for the materials ( A ) and ( B ). From
the curve:
A. ( A ) is brittle but ( B ) is ductile
B. ( A ) is ductile and ( B ) is brittle
c. Both ( A ) and ( B ) axe ductile
D. Both ( A ) and ( B ) axe brittle strain
11
515A ( 20 k g ) load is suspended from the
lower end of a wire ( 10 mathrm{cm} ) long and ( 1 mathrm{mm} )
( ^{2} ) in cross sectional area. The upper half of the wire is made of iron and the lower
half with aluminium. The total
elongation in the wire is
( left(Y_{i r o n}=20 times 10^{10} mathrm{N} / mathrm{m}^{2}, Y_{A l}=7 times 10^{10}right. )
( left.mathrm{N} / mathrm{m}^{2}right) )
A ( cdot 1.92 times 10^{-4} mathrm{m} )
B. 17.8 ( times 10^{-3} mathrm{m} )
c. ( 1.78 times 10^{-3} mathrm{m} )
D. ( 1.92 times 10^{-3} mathrm{m} )
11
516When a metallic wire is stretched with a
tension ( T_{1} ) its length is ( l_{1} ) and with a
tension ( T_{2} ) its length is ( l_{2} ). The original length of the wire is:
A. ( frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} )
в. ( frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}} )
c. ( sqrt{l_{1} l_{2}} )
D. ( frac{l_{1} l_{2}}{2} )
11
517A metallic wire of young’s modulus Y
and poisson’s ratio ( sigma ), length L and area of cross section A is stretched by a load of W kg. The increase in volume of the wire is:
( mathbf{A} cdot sigmaleft(W^{2} L / 2 A Y^{2}right) )
В ( cdot sigmaleft(W^{2} L / A Y^{2}right) )
c. ( sigmaleft(W^{2} L / 4 A Y^{2}right) )
D ( cdot sigmaleft(2 W^{2} L / A Y^{2}right) )
11
518The load versus elongation graph for
four wires of the same materials shown
in the figure. The thinnest wire is
represented by the line:
A. oc
B. OD
( c cdot O A )
D. OB
11
519A metallic rod undergoes a strain of
( 0.05 % . ) The energy stored per unit volume is ( left(Y=2 times 10^{11} mathrm{Nm}^{-2}right) )
A ( cdot 0.5 times 10^{4} mathrm{Jm}^{-3} )
B . ( 0.5 times 10^{5} mathrm{Jm}^{-3} )
c. ( 2.5 times 10^{5} mathrm{Jm}^{-3} )
D. ( 2.5 times 10^{4} mathrm{Jm}^{-3} )
11
520A wire of length ( L ) and cross-sectional ( A )
is made of a material of Young’s
modulus. If the wire is stretched by an amount ( x, ) the work done is
11
521The Young’s modulus of a wire of length and radius ( r ) is ( Y N / m^{2} . ) If the length
is reduced to ( L / 2 & ) radius to ( r / 2 ), then its Young’s modouls will be-
A ( cdot frac{Y}{2} )
B. Y
c. 2 y
D. 4Y
11
522When the tension in a metal wire is ( T_{1} )
its length is ( l_{t} ). When the tension is ( T_{2} )
its length is ( l_{2} ). The natural length of
wire is
( ^{mathbf{A}} cdot frac{T_{2}}{T_{1}}left(l_{1}+l_{2}right) )
в. ( T_{1} l_{1}+i_{2} l_{2} )
c. ( frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} )
D. ( frac{l_{T_{2}-l_{2} T_{1}}}{T_{2}+T_{1}} )
11
523A long elastic spring is stretched by ( 2 mathrm{cm} ) and its potential energy is ( U ). If the
spring is stretched by ( 10 mathrm{cm} ), the P.E., will be
A . ( 5 U )
в. ( 25 U )
c. ( U / 5 )
D. ( U / 20 )
11
524The increase in energy of a metal bar of length ‘L’ and cross-sectional area ‘A’
when compressed with a load ‘M’ along its length is (Y = Young’s modulus of the material of metal bar)
( ^{mathbf{A}} cdot frac{F L}{2 A Y} )
в. ( frac{F^{2} L}{2 A Y} )
c. ( frac{F L}{A Y} )
D ( cdot frac{F^{2} L^{2}}{2 A Y} )
11
525Assertion
The linear portion of the stress-strain
curve is the elastic region and the slope
is the modulus of elasticity or Young’s
Modulus.
Reason Young’s Modulus is the ratio of the
compressive stress to the longitudinal
strain.
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
526In the shown figure, length of the rod is
( L, ) area of cross-section ( A, ) Young’s
modulus of the material of the rod is ( Y ).
Then, ( B ) and ( A ) is subjected to a tensile
force ( boldsymbol{F}_{A} ) while force applied at end
( B, F_{B} ) is lesser than ( F_{A} ). Total change in length of the rod will be
( A )
[
F_{A} times frac{L}{2 A Y}
]
B.
[
F_{B} times frac{L}{2 A Y}
]
( c )
[
frac{left(F_{A}+F_{B}right) L}{2 A Y}
]
( D )
[
frac{left(F_{A}-F_{B}right) L}{2 A Y}
]
11
527Consider the following two statements A and B and identify the correct answer.
A) We cannot define Young’s modulus and rigidity modulus for liquids and
gases.
B) The theoretical limits of Poisson’s
ratio are 1 to 0.5
A. Both A & B are true
B. A is false but B is true
c. Both A & B are false
D. A is true but B is false
11
528The stress versus strain graphs for wi
shown in the figure. If ( Y_{A} ) and ( Y_{B} ) are
then
A. ( Y_{B}=2 Y_{A} )
B. ( Y_{A}=Y_{B} )
c. ( Y_{B}=3 Y_{A} )
D. ( Y_{A}=3 Y_{B} )
11
529A wire is suspended vertically from one of its ends is stretched by attaching a weight of ( 200 mathrm{N} ) to the lower end. The wire stretches the wire by ( 1 mathrm{mm} ). The elastic energy stored in the wire is:11
530A rubber rope of length ( 8 m ) is hung
from the ceiling of a room. What is the increase in length of rope due to its own weight? (Given : Young’s modulus of elasticity of rubber ( =mathbf{5} times mathbf{1 0 6} N / boldsymbol{m} )
and density of rubber ( =1.5 times ) ( left.mathbf{1 0}^{3} mathbf{k g} / boldsymbol{m}^{3} . text { Take } boldsymbol{g}=mathbf{1 0} boldsymbol{m} / boldsymbol{s}^{2}right) )
A ( .1 .5 mathrm{mm} )
B. ( 6 m m )
c. ( 24 m m )
D. ( 96 m m )
11
531The length of a steel wire is ( l_{1} ) when the
stretching force is ( T_{1} ) and ( l_{2} ) when the
stretching force is ( T_{2} ) The natural length of the wire is
( ^{text {A } cdot frac{l_{1} T_{1}+l_{2} T_{2}}{T_{1}+T_{2}}} )
в. ( frac{l_{2} T_{1}+l_{2} T_{2}}{T_{1}+T_{2}} )
c. ( frac{l_{2} T_{1}+l_{2} T_{2}}{T_{1}-T_{2}} )
D. ( frac{l_{2} T_{1}-l_{1} T_{2}}{T_{1}-T_{2}} )
11
532Assertion
Spring balances show incorrect
readings after using for a long time.
Reason
On using for a long time, springs in the
balances lose their elastic strength
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
533Prove ( boldsymbol{G}=frac{boldsymbol{E}}{mathbf{2}(mathbf{1}+boldsymbol{v})} )11
534From the stress against strain graph, the behavior of the wire between elastic
limit and yield point is :
A. Perfectly elastic
B. Formation of neck
c. Perfectly plastic
D. Elastic but with permanent deformation
11
535A uniform rod of length ( 60 mathrm{cm} ) and mass
( 6 k g ) is acted upon by two forces as shown in the diagram. The force exerted by ( 45 mathrm{cm} ) part of the rod on ( 15 mathrm{cm} ) part of
the rod is
A. ( 9 N )
N
В. ( 18 N )
c. ( 27 N )
D. 30N
11
536When the temperature of a gas is ( 20^{0} C )
and pressure is changed from ( boldsymbol{P}_{1}= ) ( mathbf{1 . 0 1} times mathbf{1 0}^{mathbf{5}} boldsymbol{P a} ) to ( boldsymbol{P}_{mathbf{2}}=mathbf{1 . 1 6 5} times mathbf{1 0}^{mathbf{5}} boldsymbol{P a} )
then the volume changes by ( 10 % . ) The bulk modulus is
A ( .1 .55 times 10^{5} mathrm{Pa} )
в. ( 1.05 times 10^{5} P a )
c. ( 1.4 times 10^{5} P a )
D. ( 0.115 times 10^{5} P a )
11
537The length of an elastic string is ( boldsymbol{X} boldsymbol{m} )
when the tension is ( 8 N, ) and ( Y m ) when
the tension is ( 10 N . ) The length in
metres when the tension is ( 18 N ) in
terms of ( X ) and ( Y )
11
538Two persons pull a rope towards themselves. Each person exerts a force
of ( 100 mathrm{N} ) on the rope. Find the Young
modulus of the material of the rope if it
extends in length by 1cm. (Original length of the rope ( =2 mathrm{m} ) and the area of
( operatorname{cross} operatorname{section}=2 c m^{2} )
11
539A uniformly tapering conical wire is made from a material of Young’s
modulus ( Y ) and has a normal,
unextended length ( L ). The radii, at the upper and lower ends of this conical
wire, have values ( R ) and ( 3 R )
respectively. The upper end of the wire is fixed to a rigid support and a mass ( M ) is suspended from its lower end. The equilibrium extended length,of this wire, would equal to:
A ( cdot Lleft(1+frac{1}{3} frac{M g}{pi Upsilon R^{2}}right) )
в. ( Lleft(1+frac{2}{9} frac{M g}{pi Upsilon R^{2}}right) )
c. ( _{L}left(1+frac{1}{9} frac{M g}{pi Upsilon R^{2}}right) )
D. ( Lleft(1+frac{2}{3} frac{M g}{pi Upsilon R^{2}}right) )
11
540The length of an elastic string is ( a ) metre when the longitudinal tension is ( 4 mathrm{N} ) and ( b ) metre when the longitudinal
tension is 5 N. The length of the string in metre when longitudinal tension is ( 9 N ) is :
( mathbf{A} cdot a-b )
B. ( 5 b-4 a )
c. ( 2 b-frac{1}{4} a )
D. ( 4 a-3 b )
11
541The Young’s modulus of a rubber string
( 8 mathrm{cm} ) long and density ( 1.5 mathrm{kg} / mathrm{m}^{3} ) is ( 5 times )
( 10^{8} N / m^{2}, ) is suspended on the ceiling
in a room. The increase in length due to its own weight will be:-
A ( cdot 9.6 times 10^{-5} m )
В. ( 9.6 times 10^{-11} m )
c. ( 9.6 times 10^{-3} m )
D. ( 9.6 mathrm{m} )
11
542In case of a liquid,
A. only bulk modulus is defined
B. only bulk and Young’s modulus are defined
C. only bulk and shear modulus are defined
D. Young’s modulus is defined but shear modulus is not defined
11
543The elasticity of various materials is controlled by its
A. Ultimate tensile stress
B. Stress at yield point
c. Stress at elastic limit
D. Tensile stress
11
544The load versus elongation graph for four wires of the same material and
same length is shown in the figure.
The thinnest wire is represented by the
ine
( A cdot O A )
B. OB
( c cdot 0 c )
D. o
11
545A wire stretches by a certain amount under a load. If the load ( & ) radius both
are increased to 4 time. Find the stress
cause in the wire.
11
546A petite young woman of ( 50 k g ) distributes her weight equally over her high-heeled shoes. Each heel has an area of ( 0.75 mathrm{cm}^{2} . ) Find the pressure
exerted by each heel? Take ( g=10 m / s^{2} )
A ( .6 .66 times 10^{6} P a )
B . ( 3.33 times 10^{6} P a )
c. ( 1.67 times 10^{6} P a )
D. ( 4.44 times 10^{6} mathrm{Pa} )
11
547A wire suspended from one end carries a sphere at its other end. The elongation in the wire reduces from 2mm to
1.6 ( m m ) on completely immersing the sphere in water. The density of the material of the sphere is
A. ( 3200 mathrm{kg} / mathrm{m}^{3} )
в. ( 800 mathrm{kg} / mathrm{m}^{3} )
c. ( 1250 mathrm{kg} / mathrm{m}^{3} )
D. ( 5000 mathrm{kg} / mathrm{m}^{3} )
11
548Two wires of the same material and
same mass are stretched by the same
force. Their length are in the ratio 2: 3
Their elongations are in the ratio
A .3: 2
B. 2: 3
c. 4: 9
D. 9: 4
11
549The difference between pressure and
stress is
A. pressure and stress have different units
B. pressure and stress have different dimensions
C. Force cannot be determined using stress, but in pressure it can be done
D. Pressured is applied to a body, while stress is induced
11
550In the figure shown, the plastic region
occurs
A. Before point ( A )
B. Beyond point A
c. Between points A and
D. Between points D and E
11
551When a weight of ( 10 mathrm{kg} ) is suspended
from a copper wire of length ( 3 m ) and diameter 0.4 mm. Its length increases
by ( 2.4 mathrm{cm} . ) If the diameter of the wire is doubled, then the extension is its length
will be :
A ( .7 .6 mathrm{cm} )
в. ( 4.8 mathrm{cm} )
c. ( 1.5 mathrm{cm} )
D. ( 0.6 mathrm{cm} )
11
552If Young modulus is three times of modulus of rigidity, then Poisson ratio is equal to:
A . 0.2
B. 0.3
( c .0 .4 )
D. 0.5
11
553Poisson’ ratio is defined as the ratio of
A. longitudinal stress and longitudinal strain
B. Iongitudinal stress and lateral stress
C. lateral stress and longitudinal stress
D. lateral stress and lateral strain
11
554A metal block is experiencing an atmospheric pressure of ( 1 times 10^{5} N / m^{2} )
when the same block is placed in a vaccum chamber the fractional change in its volume is (the bulk modulus of
metal is ( left.1.25 times 10^{11} N / m^{2}right) )
A ( cdot 4 times 10^{-7} )
В. ( 2 times 10^{-7} )
c. ( 8 times 10^{-7} )
D. ( 1 times 10^{-7} )
11
555What amount of work is done in
increasing the length of a wire through unity?
A ( cdot frac{Y L}{2 A} )
в. ( frac{Y L^{2}}{2 A} )
c. ( frac{Y A}{2 L} )
D. ( frac{Y L}{A} )
11
556Two elastic wire ( A & B ) having length
( ell_{A}=2 m ) and ( ell_{B}=1.5 m ) and the ratio
of young’s modules ( Y_{A}: Y_{B} ) is ( 7: 4 . ) If
radius of wire ( Bleft(r_{B}right) ) is ( 2 m m ) then
choose the correct value of radius of
wire ( A . ) Given that due to application of
the same force charge in length in both ( A & B ) is same
A. ( 1.7 m m )
в. ( 1.9 m m )
( c .2 .7 m m )
D. ( 2 m m )
11
557Assertion
The stress-strain relationship in elastic region need not be linear and can be
non-linear.
Reason
Steel has non linear,profile in elastic
zone
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
558The stress-strain graphs are shown in
the figure for two materials ( A ) and ( B ) are
shown in figure. Young’s modulus of ( boldsymbol{A} )
is greater than that of ( B ).
Reason
The Young’s modules for small strain is, ( Y=frac{text {stress}}{text {strain}}= ) slope of linear portion of
graph; and slope of ( A ) is more than that
of ( B )
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
11
559Which of the following is an example of plastic deformation?
A. stretching a rubber band
B. stretching saltwater taffy
c. none
D. both
11
560A rubber cord catapult has crosssection area ( 25 m m^{2} ) and initial length of rubber cord is ( 10 mathrm{cm} ). It is stretched to
( 5 c m ) and then released to project a
missile of mass 5gm. Taking, ( boldsymbol{Y}_{text {rubber}}= )
( 5 times 10^{8} N / m^{2}, ) velocity of projected
missile is
A ( cdot 20 m s^{-1} )
B. ( 100 mathrm{ms}^{-1} )
( mathbf{c} cdot 250 m s^{-1} )
D. ( 200 m s^{-1} )
11
561The stress-strain graph for a metal wire is as shown in the figure. In the graph, the region in which Hooke’s law is
obeyed, the ultimate strength and
fracture points are represented by
A. ( O A, C, D )
в. ( O B, D, E )
c. ( O A, D, E )
D. ( O B, C, D )
11
562A man grows into a giant such that his linear dimensions increases by a factor of ( 9 . ) Assuming that his density remains same, the stress in the leg will change
by a factor of the
A ( cdot frac{1}{81} )
B. 9
( c cdot frac{1}{9} )
D. 81
11
563Define elasticity.11
564If in a wire of Young’s modulus ( Y )
longitudinal strain ( X ) is produced then
the potential energy stored in its unit volume will be :
A. ( 0.5 Y X^{2} )
2
В. ( 0.5 Y^{2} X )
c ( .2 Y X^{2} )
D. ( Y X^{2} )
11
565A steel ring of radius ( r ) and cross
sectional area ( A ) is fitted on to a wooden
disc of radius ( boldsymbol{R}(boldsymbol{R}>boldsymbol{r}) . ) If Young;s
modulus be ( Y ), then the force with
which the steel ring is expanded, is
( ^{mathbf{A}} cdot_{A Y} frac{R}{r} )
в. ( quad A Yleft(frac{R-r}{r}right) )
c. ( frac{Y(R-r)}{A} frac{r}{r} )
D. ( frac{Y r}{A R} )
11
566Young’s modulus of rubber is ( 10^{4} N / m^{2} )
and area of cross section is ( 2 mathrm{cm}^{-2} ). If
force of ( 2 times 10^{5} ) dyn is applied along its
length, then its initial ( l ) becomes.
A . ( 3 l )
в. ( 4 l )
( c cdot 2 l )
D. None of these
11
567A wire ( 1 m ) long has cross-section
( 1 m m^{2} ) and ( Y=1.2 times 10^{11} P a . ) Find the
work done in stretching it by ( 2 m m )
A . 2.4
B. 0.24J
c. 0.024J
D. 1.2.
11
568A 5 metre long wire is fixed to the
ceiling. A weight of ( 10 k g ) is hung at the
lower end and is 1 metre above the floor.
The wire was elongated by 1 mm. The energy stored in the wire due to stretched is
A . zero
B. 0.05joule
c. 100 joule
D. 500 joule
11
569A toy car travels in a horizontal circle of
radius ( 2 a, ) kept on the track by a radial elastic string of unstretched length a. The period of rotation is T. Now the car
is speeded up until it is moving in a circle of radius 3 a. Assuming that the string obeys Hooke’s law then the new period will be
A ( cdot sqrt{frac{4}{3}} T )
B ( cdot frac{3^{2}}{3^{3}} T )
c. ( sqrt{frac{3}{2}} T )
D. ( frac{3}{4} T )
11
570Assertion
To increase the length of a thin steel
wire of ( 0.1 mathrm{cm}^{2} ) cross sectional area by
( 0.1 %, ) a force of ( 2000 N ) is required, its
( boldsymbol{Y}=mathbf{2 0 0} times mathbf{1 0}^{mathbf{9}} boldsymbol{N} boldsymbol{m}^{-mathbf{2}} )
Reason
It is calculated by ( Y=frac{boldsymbol{F} times boldsymbol{L}}{boldsymbol{A} times boldsymbol{Delta} boldsymbol{L}} )
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
571The stress strain curve for two metals ( A )
and ( mathrm{B} ) are as shown in the figure. then
A. A is ductile while B is brittle
B. A is brittle while B is ductile
c. Both ( A ) and ( B ) are ductile
D. Both A and B are brittle
11
572Two exactly similar wires of steel and copper are stretched by equal forces. If the total elongation is ( 2 mathrm{cm}, ) then how much is the elongation in steel and
copper wire respectively? Given ( Y_{text {steel}} ) ( =20 times 10^{11} mathrm{dyne} / mathrm{cm}^{2}, Y_{text {copper}}=12 times 10^{11} )
dyne /cm ( ^{2} )
A . ( 1.25 mathrm{cm} ; 0.75 mathrm{cm} )
B. 0.75 ( mathrm{cm} ; 1.25 mathrm{cm} )
c. ( 1.15 mathrm{cm} ; 0.85 mathrm{cm} )
D. ( 0.85 mathrm{cm} ; 1.15 mathrm{cm} )
11
573The ratio of change in dimension at right angles to applied force to the initial dimension is defined as
A. ( Y )
B. ( eta )
( c cdot beta )
D. ( K )
11
574The following four wires are made of the same material. Which of these will have
the largest extension when the same tension is applied?
A. Length ( =50 mathrm{cm}, ) diameter ( =0.5 mathrm{mm} )
B. Length = 100 cm, diameter = 1 mm
c. Length( =200 mathrm{cm}, ) diameter ( =2 mathrm{mm} )
D. Length ( =300 mathrm{cm}, ) diameter ( =3 mathrm{mm} )
11
575A force of ( 15 N ) increases the length of a wire by ( 1 mathrm{mm} . ) The additional force required to increase the length by
( 2.5 m m ) in ( N ) is
A . 22.5
в. 37.5
c. 52.5
D. 75
11
576Q Type your question
columns each of length ( l ), cross
sectional radius ( r ) and young’s
modulus ( Y ). What should be the
minimum cross – section radius ( r, ) so
that the beam bearing more load, can
escape from buckling?
( left(frac{m g l^{2}}{pi^{3} Y}right)^{1 / 4} )
( ^{mathrm{B}}left(frac{2 m g l^{2}}{3 pi^{3} Y}right)^{1 / 4} )
( left(frac{m g l^{2}}{3 pi^{3} Y}right)^{1 / 4} )
( left(frac{3 m g l^{2}}{2 pi^{3} Y}right)^{1 / 4} )
11
577What is the change in the volume of 1.0 L kerosene, when it is subjected to an extra pressure of ( 2.0 times 10^{5} N m^{-2} ) from
the following data? Density of kerosene ( =800 mathrm{kg} mathrm{m}^{-3} ) and speed of sound in kerosene ( =1330 mathrm{ms}^{-1} )
( A cdot 0.97 mathrm{cm}^{-3} )
B. ( 0.66 mathrm{cm}^{-3} )
c. ( 0.15 mathrm{cm}^{-3} )
D. ( 0.59 mathrm{cm}^{-3} )
11
578A ( 20 k g ) load is suspended from the
lower end of a wire ( 10 mathrm{cm} ) long and ( 1 mathrm{mm} )
( ^{2} ) in cross sectional area. The upper half of the wire is made of iron and the lower
half with aluminium. The total
elongation in the wire is
( left(Y_{i r o n}=20 times 10^{10} mathrm{N} / mathrm{m}^{2}, Y_{A l}=7 times 10^{10}right. )
( left.mathrm{N} / mathrm{m}^{2}right) )
A ( cdot 1.92 times 10^{-4} mathrm{m} )
B. 17.8 ( times 10^{-3} mathrm{m} )
c. ( 1.78 times 10^{-3} mathrm{m} )
D. ( 1.92 times 10^{-3} mathrm{m} )
11
579A steel wire with cross section ( 3 mathrm{cm}^{2} )
has elastic limit ( 2.4 times 10^{8} ) Pa. Find the
maximum upward acceleration that can be given to a ( 1200 k g ) elevator supported by this cable if the stress is not to exceed ( 1 / 3 r d ) of the elastic limit
( mathbf{A} cdot 9 m s^{-2} )
B. ( 10 mathrm{ms}^{-2} )
( mathrm{c} cdot 11 mathrm{ms}^{-2} )
D. ( 12 mathrm{ms}^{-2} )
11
580A steel cable with a radius of ( 1.5 mathrm{cm} ) supports a chairlift at a ski area. If the
maximum stress is not to exceed
( 10^{8} N m^{-2}, ) what is the maximum load
the cable can support?
11
581Two opposite forces ( boldsymbol{F}_{1}= )
( 120 N ) and ( F_{2}=80 N ) act on an heavy
elastic plank of modulus of elasticity ( boldsymbol{y}=boldsymbol{2} times mathbf{1 0}^{11} boldsymbol{N} / boldsymbol{m}^{2} ) and length ( boldsymbol{L}=mathbf{1} boldsymbol{m} )
placed over a smooth horizontal surface. The cross-sectional area of
plank is ( A=0.5 m^{2} . ) If the change in the
length of plank is (in ( mathrm{nm} ) )
( A )
B. 0.5
( c cdot 5 )
( D )
11
582A wire of cross section ( A ) is stretched
horizontally between two clamps located ( 2 l ) m apart. A weight ( W ) kg is suspended from the mid-point of the wire. If the mid-point sags vertically through a distance ( x<1 ) the strain produced is
A ( cdot frac{2 x^{2}}{l^{2}} )
в. ( frac{x^{2}}{l^{2}} )
c. ( frac{x^{2}}{2 l^{2}} )
D. None of these
11
583How much pressure should be applied on a litre of water if it is to be
compressed by ( 0.1 % ? ) (Bulk moduls of water ( =2100 M P a) )
A ( .2100 k P a )
в. ( 210 k P a )
c. ( 2100 M P a )
D. ( 210 M P a )
11
584A rigid bar of mass ( 15 k g ) is supported
symmetrically by three wires each ( 2 m ) long. Those at each end are of copper and the middle one is of iron. Determine
the ratio of their diameters if each is to
have the tension? (Given E for copper =
( 110 times 10^{9} N / m^{2} ) and ( E ) for iron ( =190 times )
( mathbf{1 0}^{mathbf{9}} mathbf{N} / boldsymbol{m}^{mathbf{2}} )
A . 12.6: 2
в. 1.31: 1
c. 4.65: 3
D. 2.69 : 4
11
585A solid sphere of radius ( R ) made of a
material of bulk modulus ( K ) is
surrounded by a liquid in cylindrical
container. A massless piston of area ( boldsymbol{A} ) floats on the surface of the liquid. When
a mass ( M ) is placed on the piston to compress the liquid, the fractional change in the radius of the sphere,
( delta R / R, ) is
11
586A spring with force content ( k ) is initially
stretched by ( x_{1} . ) If it is further stretched
by ( x_{2}, ) then the increase in its potential
energy is.
A ( cdot frac{1}{2} kleft(x_{2}^{2}-x_{1}^{2}right) )
B ( cdot frac{1}{2} k x_{2}left(x_{2}-2 x_{1}right) )
( mathbf{c} cdot frac{1}{2} k x_{1}^{2}-frac{1}{2} k x_{2}^{2} )
D・frac{ } { frac { 1 } { 2 } } x _ { 1 } ( x _ { 1 } + x _ { 2 } ) ^ { 2 }
11
587Plastic deformation results from the
following
A. Slip
B. Twinning
c. Both slip and twinning
D. creep
11
588A wire suspended vertically from one of its ends stretched by attaching a
weight of ( 200 N ) to the lower end. The
weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is:
A. 0.25
J ( J )
в. ( 10 J )
( c .20 J )
D. ( 0.1 J )
11
589A beam of metal supported at the two edges is loaded at the centre. The depression at the centre is proportional
to
( mathbf{A} cdot Y^{2} )
в. ( Y )
c. ( 1 / Y )
D. ( 1 / Y^{2} )
11
590A uniform cube is subjected to volume compression. Each side gets decreased by ( 1 %, ) then the bulk strain is
A . 0.01
B. 0.03
c. 0.06
D. 0.09
11
591An iron rod of length ( 2 mathrm{m} ) and cross sectional area of ( 50 mathrm{mm}^{2} ) stretched by
0.5mm, when a mass of 250 kgis hung from its lower end. Young’s modulus of
iron rod is
( mathbf{A} cdot 19.6 times 10^{20} N / m^{2} )
B . ( 19.6 times 10^{18} N / m^{2} )
C ( cdot 19.6 times 10^{10} N / m^{2} )
D. ( 19.6 times 10^{15} N / m^{2} )
11
592A fixed volume of iron is drawn into a wire of length ( l ). The extension produced
in this wire by a constant force ( boldsymbol{F} ) is
proportional to :
A ( cdot frac{1}{l^{2}} )
B. ( frac{1}{l} )
( c cdot l^{2} )
D. ( l )
11
593For which of the following is the modulus of rigidity highest?
A. glass
B. quartz
c. rubber
D. water
11
594When a tension ( F ) is applied, the
elongation produced in uniform wire of length ( L, ) radius ( r ) is ( e . ) When tension ( 2 F )
is applied, the elongation produced in another uniform wire of length ( 2 L ) and
radius ( 2 r ) made of same material is:
A . ( 0.5 e )
B. ( 1.0 e )
c. ( 1.5 e )
D. ( 2.0 e )
11
595A steel wire of diameter ( d=1.0 ) mm is
stretched horizontally between two clamps located at the distance ( l= ) ( 2.0 m ) from each other. A weight of mass
( boldsymbol{m}=mathbf{0 . 2 5} boldsymbol{k g} ) is suspended from the
midpoint ( O ) of the wire. What will the
resulting descent of the point ( O ) be in millimetres?E=2 ( times 10^{11} N / m^{2} )
11
596Assertion
Stress is the internal force per unit area
of a body.
Reason
Rubber is more elastic than steel.
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
597Point out the wrong statement about the magnetic properties of soft iron and
steel
A. Retentivity of soft iron is more than retentivity of stee
B. Coercivity of soft iron is less than coercivity of steel
c. Area of B-H loop in soft iron is smaller than the area of B-H loop for steel
D. Area of B-H loop in soft iron is greater than the area of B-H loop for steel
11
598A cast iron column has an internal
diameter of 200 mm. What should be
the minimum external diameter (in
( mathrm{m} ) so that it may carry a load of
1.6 million ( N ) without the stress
exceeding ( 90 N / m m^{2} ? ) (round off your answer to nearest integer)
11
599The Young’s modulus of a wire of length
( L ) and radius ( r ) is ( Y ). If the length is
reduced to ( frac{L}{2} ) and radius is ( frac{r}{2}, ) then the Young’s modulus will be
A ( frac{Y}{2} )
в. ( Y )
( c .2 Y )
D. ( 4 Y )
11
600Shearing stress causes change in
A . Length
B. Breadth
c. shape
D. Volume
11
601Select the correct alternative(s).
A. Elastic forces are always conservative
B. Elastic forces are not always conservative
C. Elastic forces are conservative only when Hooke’s law is obeyed
D. Elastic forces may be conservative even when Hooke’s law is not obeyed
11
602Three equal masses ( 3 k g ) are connected
by massless string of cross-sectional
area ( 0.005 c m^{2} ) and Young’s modulus
( 2 times 10^{11} N m^{2} . ) In the absence of friction
the longitudinal strain in the wire:
( mathbf{A} cdot A ) is ( 10^{-4} )
B. ( B ) is ( 2 times 10^{-4} )
( c . ) Both a and ( b )
D. None of these
11
603A copper wire of length ( 2.4 m ) and a steel
wire of length ( 1.6 m, ) both the diameter
( 3 m m, ) are connected end to end. When
stretched by a load, the net elongation is found to be ( 0.7 m m ). The load applied
is
( left(boldsymbol{Y}_{text {copper}}=mathbf{1 . 2} times mathbf{1 0}^{mathbf{1 1}} mathbf{N} quad boldsymbol{m}^{-2}, boldsymbol{Y}_{text {steel}}=right. )
A . ( 1.2 times 10^{2} N )
B. ( 1.8 times 10^{2} N )
c. ( 2.4 times 10^{2} N )
D. ( 3.2 times 10^{2} N )
11
604A cube of sponge rubber with edge length ( 5 mathrm{cm} ) has a force of ( 2 mathrm{N} ) applied horizontally to the top face (parallel to an edge) while the bottom face is held fixed. If the top face is displaced horizontally through a distance of ( 1 mathrm{mm} ) find the shear modulus for the sponge rubber.
A. ( S=7 times 10^{4} N m^{-2} )
B. ( S=6 times 10^{4} N m^{-2} )
c. ( S=4 times 10^{4} N m^{-2} )
D. ( S=5 times 10^{4} N m^{-2} )
11
605Two wires of the same material (young’s modules ( Y ) ) and same length ( L ) but radii
( R ) and ( 2 R ) respectively are joined end to
end and a weight ( W ) is suspended from
the combination as shown in the figure.
the elastic potential energy in the system in equilibrium is
A ( cdot frac{3 W^{2} L}{4 pi R^{2} Y} )
В ( cdot frac{3 W^{2} L}{8 pi R^{2} Y} )
( ^{mathbf{C}} cdot frac{5 W^{2} L}{8 pi R^{2} Y} )
( ^{mathrm{D}} cdot frac{W^{2} L}{pi R^{2} Y} )
11
606On stretching a wire, the elastic energy stored per unit volume is
A. ( F l / 2 A L )
в. ( F A / 2 L )
c. ( F L / 2 A )
D. ( F L / 2 )
11
607A uniform cube is subjected to volume compression. If each side is decreased by ( 1 % ), then bulk strain is :
A . 0.01
B. 0.06
( c .0 .02 )
D. 0.03
11
608When the load on a wire is slowly increased from 3 to ( 5 k g w t, ) the
elongation increases from 0.61 to 1.02mm. The work done during the extension of wire is
( mathbf{A} cdot 0.16 J )
в. ( 0.016 J )
c. 1.6 .5
D. 16.5
11
609A stone of mass ( m ) tied to one end of a
wire of length ( L ). The diameter of the
wire is ( D ) and it is suspended vertically. The stone is now rotated in a horizontal
plane and makes an angle ( theta ) with the
vertical. If Young’s modulus of the wire
is ( Y, ) then the increase in the length of
the wire is then
( ^{mathbf{A}} cdot frac{4 m g L}{pi D^{2} Y} )
B. ( frac{4 m g L}{pi D^{2} Y sin theta} )
c. ( frac{4 m g L}{pi D^{2} Y cos theta} )
D. ( frac{4 m g L}{pi D^{2} Y tan theta} )
11
610A steel wire of length ( 30 mathrm{cm} ) is stretched ti increase its length by ( 0.2 mathrm{cm} ). Find the lateral strain in the wire if the poisson’s ratio for steel is 0.19:
A . 0.0019
B. 0.0008
c. 0.019
D. 0.008
11
611The ability of the material to deform without breaking is called:
A. Elasticity
B. Plasticity
c. Creep
D. None of these
11
612The force required to double the length of a steel wire of area of cross-section
( 5 times 10^{-5} m^{2}(text { in } N) ) is :
( left(Y=20 times 10^{10} P aright) )
A . ( 10^{7} )
B . ( 10^{6} )
( mathrm{c} cdot 10^{-7} )
D. ( 10^{5} )
11
613A wire of cross section ( A ) is stretched
horizontally between two clamps
located ( 2 l m ) apart. A weight ( W k g ) is suspended from the mid-point of the wire.If the Young’s modulus of the
material is ( Y, ) the value of extension ( x )
is
( ^{mathrm{A}} cdotleft(frac{W l}{Y A}right)^{1 / 3} )
( mathbf{B} cdotleft(frac{Y A}{W I}right)^{1 / 3} )
c. ( frac{1}{l}left(frac{W l}{Y A}right)^{2 / 3} )
( ^{mathrm{D}} cdotleft(frac{W}{Y A}right)^{2 / 3} )
11
614Define stress and explain the types of
stress
11
615A load of ( 10 mathrm{kg} ) is suspended by a metal
wire 3 m long and having a cross-
sectional are ( 4 m m^{2} . ) Find (a) the stress
(b) the strain and
(c) the elongation.
Young modulus of the metal is ( 2.0 times ) ( 10^{11} N m^{-2} )
11
616A wire elengates by Imm when a weight w is hanged than it. If wire goes over a pulley and 2 weights W each are huge at two ends. What will be elongations of wire is mm?11
617A ( 30.0 mathrm{kg} ) hammer, moving with speed speed ( 20.0 m s^{-1}, ) strikes a steel Spike
( 2.30 mathrm{cm} ) in diameter. The hammer
rebounds with speed ( 10.0 mathrm{ms}^{-1} ) after
0.110 s.What is the average Strain in the Spike during the impact?
11
618A metal rod of Young’s modulus ( 2 times ) ( 10^{10} N m^{-2} ) undergoes an elastic strain
of ( 0.06 % ). The energy per unit volume stored in ( J m^{-3} ) is
A. 3600
в. 7200
c. 10800
D. 14400
11
619If a wire having initial diameter of ( 2 m m )
produced the longitudinal strain of 0.1
( %, ) then the final diameter of wire is
( (sigma=mathbf{0 . 5}) )
A ( .2 .002 m m )
B. ( 1.999 mathrm{mm} )
c. ( 1.998 mathrm{mm} )
D. ( 2.001 m m )
11
620Longitudinal strain is possible in:
A . Gases
B. Liquids
c. Solids
D. All of these
11
621Assertion (A) : The elastic potential energy of a spring increases when it is elongated and decreases when it is
compressed
Reason
(R) : Work done on spring is stored in it as elastic potential energy.
A. Both assertion and reason are true and the reason is correct explanation of the assertion
B. Both assertion and reason are true, but reason is not correct explanation of the assertion
c. Assertion is true, but the reason is false
D. Assertion is false, but the reason is true
11
622The radii and Young’s modulus of two uniform wires ( A & B ) are in the ratio
2: 1 and 1: 2 respectively. Both the
wires are subjected to the same longitudinal force. If increase in the length of wire ( A ) is ( 1 % ). Then the
percentage increase in length of wire ( B ) is :
A . 1
в. 1.5
( c cdot 2 )
( D )
11
623Four wires ( P, Q, R ) and ( S ) of same
materials have diameters and
stretching forces as shown
below. Arrange their strains in the
decreasing order.
( begin{array}{lll}text { Wire } & text { Diameter } & text { Stretching force } \ mathrm{P} & 2 mathrm{mm} & 10 mathrm{N} \ mathrm{Q} & 1 mathrm{mm} & 20 mathrm{N} \ mathrm{R} & 4 mathrm{mm} & 30 mathrm{N} \ mathrm{S} & 3 mathrm{mm} & 40 mathrm{N}end{array} )
( A )
( mathrm{Q}, mathrm{S}, mathrm{P}, mathrm{R} )
B. R,P,S,Q
( mathbf{c} . ) P,Q,R,S
D. ( P, R, Q, S )
11
624A spring with spring constants K when compressed by ( 1 mathrm{cm} ), the potential energy stored is U.If it is further
compressed by ( 3 mathrm{cm}, ) then its final potential energy is
A . ( 16 U )
в. ( 9 U )
c. ( 8 U )
D. ( 15 U )
11
625Two copper wires having the length in ratio 4: 1 and their radii ratio as 1: 4
are stretched by the same force. Then the ratio of the longitudinal strain in the two will be
( mathbf{A} cdot 1: 16 )
B. 16: 1
( mathbf{c} cdot 1: 64 )
D. 64: 1
11
626A steel cylindrical rod of length ( l ) and
radius ( r ) is suspended by its end from the ceiling. Find the elastic deformation
energy ( U ) of the rod.
A ( cdot U=frac{1}{6} pi r^{2} rho^{2} g^{2} frac{l^{3}}{E} )
B. ( U=frac{5}{6} pi r^{2} rho^{2} g^{2} frac{l^{3}}{E} )
( ^{mathrm{C}} U=frac{1}{6} pi r^{2} rho^{2} g^{2} frac{2 l^{3}}{E} )
D. ( U=frac{5}{6} pi r^{2} rho^{2} g^{2} frac{2 l^{3}}{E} )
11
627Breaking stress of a material is ( 2 times ) ( 10^{8} N / m^{2} . ) What maximum length of
the wire of this material can be so that the wire does not break my own weight? [Density of material ( =mathbf{5} times mathbf{1 0}^{mathbf{3}} mathbf{k g} / mathbf{m}^{mathbf{3}} mathbf{]} )
A. ( 1 k m )
B. ( 2 mathrm{km} )
( c .3 k m )
D. ( 4 k m )
11
628Volume of a liquid when compressed by additional pressure of ( 10^{5} N / m^{2} ) is 196
cc and when compressed by a pressure of ( 1.5 times 10^{5} N / m^{2}, ) the volume is ( 194 c c )
The bulk modulus of the liquid is:
A ( cdot 10^{5} N / m^{2} )
B . ( 1.5 times 10^{6} )
c. ( 5 times 10^{5} N / m^{2} )
D. ( 5 times 10^{6} N / m^{2} )
11
629During unloading beyond ( B ), say ( C ), the
length at zero stress is now equal to:
A. less than original length
B. greater than original length
c. original length
D. can’t be predicted
11
630To determine the Young modulus of a wire, several measurements are taken.
In which row can the measurement not
be taken directly with the stated apparatus?
A. measurement: area of cross-section of wire apparatus : micrometer screw gauge
B. measurement: extension of wire ; apparatus: vernier scale
c. measurement: mass of load applied to wire ; apparatus : electronic balance
D. measurement: original length of wire ; apparatus metre rule
11
631The Young’s modulus of a material is
( 2 times 10^{11} N / m^{2} ) and its elastic limit is
( 1.8 times 10^{8} N / m^{2} . ) For a wire of ( 1 m ) length
of this material, the maximum elongation achievable is
( mathbf{A} cdot 0.2 m m )
в. ( 0.3 m m )
( c .0 .4 m m )
D. ( 0.5 m m )
11
632The stress required to double the length of a wire of Young’s modulus ( boldsymbol{E} ) is :
A ( .2 E )
в. ( E )
c. ( E / 2 )
D. ( 3 E )
11
633Two wires of the same radius and
material and having length in the ratio 8.9: 7.6 are stretched by the same
force. The strains produced in the two cases will be in the ratio:
A . 1: 1
B. 8.9: 1
c. 1: 7.6
D. 1: 3.2
11
634Which of the following statements is
incorrect?
A. When a material is under tensile stress, the restoring forces are caused by interatomic attraction while under compressional stress, the restoring force is due to interatomic repulsion
B. The stretching of a coil is determined by its shear modulus
C. Rubber is more elastic than steel
D. Shearing stress plays an important role in the buckling of shafts
11
635A steel wire can support a maximum
load of ( W ) before reaching its elastic limit. How much load can another wire,
made out of identical steel, but with a
radius one half the radius of the first wire, support before reaching its elastic limit.?
( mathbf{A} cdot W )
в. ( frac{W}{2} )
c. ( frac{w}{4} )
D. ( 4 W )
11
636Poisson’s ratio cannot exceed
A . 0.25
B. 1.0
c. 0.75
D. 0.5
11
637A solid sphere of radius ( boldsymbol{R}, ) made up of a
material of bulk modulus ( boldsymbol{K} ) is
surrounded by a liquid in a cylindrical
container. A massless piston of area ( boldsymbol{A} )
floats on the surface of the liquid. When
a mass ( M ) is placed on the piston to
compress the liquid, the fractional
change in the radius of the sphere is
( mathbf{A} cdot frac{M g}{2 A K} )
в. ( frac{M g}{3 A K} )
c. ( frac{M g}{A K} )
D. ( frac{2 M g}{3 A K} )
11
638The energy stored per unit volume in copper wire, which produces longitudinal strain of ( 0.1 % ) is:
( left(boldsymbol{Y}=mathbf{1 . 1} times mathbf{1 0}^{mathbf{1 1}} boldsymbol{N} / boldsymbol{m}^{2}right) )
A ( cdot 11 times 10^{3} mathrm{J} / mathrm{m}^{3} )
В . ( 5.5 times 10^{3} J / m^{3} )
( mathbf{c} cdot 5.5 times 10^{4} J / m^{3} )
D. ( 11 times 10^{4} J / m^{3} )
11
639A uniform rod of mass ( m ), length ( L ), area
of cross-section ( A ) is rotated about an
axis passing through one its ends and perpendicular to its length with constant angular velocity ( omega ) in a
horizontal plane. If ( Y ) is the Young’s modulus of the material of rod, the
increase in its length due to rotation of
rod is:
( ^{A} cdot frac{m omega^{2} L^{2}}{A Y} )
в. ( frac{m omega^{2} L^{2}}{2 A Y} )
( ^{mathbf{C}} cdot frac{m omega^{2} L^{2}}{3 A Y} )
D. ( frac{2 m omega^{2} L^{2}}{A Y} )
11
640A wire of length ( L ) has a linear mass
density ( mu ) and area of cross-section ( boldsymbol{A} ) and Young’s modulus ( Y ) is suspended vertically from a rigid support. The extension produced in the wire due to its own weight is:
( ^{text {A } cdot frac{mu g L^{2}}{Y A}} )
в. ( frac{mu g L^{2}}{2 Y A} )
c. ( frac{2 mu g L^{2}}{Y A} )
D ( cdot frac{2 mu g L^{2}}{3 Y A} )
11
641A wire extends by ‘I’ on the application of load ‘mg’. Then, the energy stored in it is :
A ( . m g l )
в. ( frac{m g l}{2} )
( c cdot frac{m g}{l} )
D ( cdot m g l^{2} )
11
642A ( 20 k g ) load is suspended by a wire of
( operatorname{cross} operatorname{section} 0.4 m m^{2} . ) The stress
produced in ( mathrm{N} / mathrm{m}^{2} ) is :
( A cdot 4.9 times 10^{-6} )
B. ( 4.9 times 10^{8} )
( c cdot 49 times 10^{8} )
D. 2.45 times 10 ( ^{-6} )
11
643The average depth of Indian Ocean is about ( 3000 m ). The fractional
compression, ( frac{Delta V}{V} ) of water at the
bottom of the ocean is then
(Given: Bulk modulus of the water=
( 2.2 times 10^{9} N m^{-2} ) and ( g=10 m s^{-2} )
( mathbf{A} cdot 0.82 % )
B . ( 0.91 % )
c. ( 1.36 % )
D. 1.24%
11
644A uniform ring of radius ( R ) and made up of a wire ofcross-sectional radius r is
rotated about its axis witha frcquency If density of the wire is p and Young’s modulus is ( Y ). Find the fractional change in radiusof the ring.
11
645When temperature of ( operatorname{gas} ) is ( 20^{circ} mathrm{C} ) and pressure is changed from ( P_{1}=1.01 times 10^{5} )
Pa to ( P_{2}=1.165 times 10^{5} ) Pa then the volume
changed by ( 10 % ). the bulk modulus is:
A ( .1 .55 times 10^{5} P a )
В. ( 0.155 times 10^{5} P a )
c. ( 15.5 times 10^{5} P a )
D. ( 155 times 10^{5} P a )
11
646Which one of the following substance possesses the highest elasticity?
A . rubber
B. glass
c. steel
D. copper
11
647A steel bar ( A B C D 40 c m ) long is made
up of three parts ( A B, B C ) and ( C D, ) as
shown in the figure The rod is subjected
to a pull of ( 25 k N . ) The total extension of
the rod is (Young’s modulus for steel
( 2 times 10^{11} N m^{-2} )
( mathbf{A} cdot 0.0637 m m )
B. ( 0.0647 mathrm{mm} )
c. ( 0.0657 m m )
D. ( 0.0667 m m )
11
648What is the tension of each wire?
A . ( 25 N )
в. ( 50 N )
( c .75 N )
D. ( 100 N )
11
649A solid sphere of radius ( R ) made of a
material of bulk modulus B surrounded
by a liquid in a cylindrical container.A massless piston of area A floats on the surface of the liquid. Find the fractional decreases in the radius of the sphere
( left(frac{d R}{R}right) ) when a mass ( M ) is placed on the
piston to compress the liquid:
A ( cdotleft(frac{3 M g}{A B}right) )
B ( cdotleft(frac{2 M g}{A B}right) )
( ^{mathbf{c}} cdotleft(frac{M g}{3 A B}right) )
D. ( left(frac{M g}{2 A B}right) )
11
650The stress-strain graphs for materials and B are shown in Fig. The graphs are drawn to the same scale.
(a) Which of the materials has the
greater Young’s modulus?
(b) Which of the two is the stronger material?
11
651Two strips of metal are riveted together at their ends by four rivets, each of
diameter 6 m ( m ). Assume that each rivet
is to carry one quarter of the load. If the shearing stress on the rivet is not to exceed ( 6.9 times 10^{7} P a ), the maximum
tension that can be exerted by the riveted strip is then
A ( cdot 2 times 10^{3} N )
B. ( 3.9 times 10^{3} N )
c. ( 7.8 times 10^{3} N )
D. ( 15.6 times 10^{3} N )
11
652The Young’s modulus of the material of
the wire of length ( L ) and radius ( r ) is
( boldsymbol{Y} boldsymbol{N} / boldsymbol{m}^{2} . ) If the length is reduced to ( boldsymbol{L} / mathbf{2} )
and radius ( r / 2 ), the Young’s modulus
will be:
A ( cdot frac{Y}{2} )
в. ( Y )
( c .2 Y )
D. ( 4 Y )
11
653Uniform rod of mass ( m ), length ( l ), area of
cross-section ( boldsymbol{A} ) has Young’s modulus ( boldsymbol{Y} ) If it is hanged vertically, elongation under its own weight will be :
( ^{text {A }} cdot frac{m g l}{2 A Y} )
в. ( frac{2 m g l}{A Y} )
c. ( frac{m g l}{A Y} )
D. ( frac{m g Y}{A l} )
11
654Assume that if the shear stress in stee
exceeds about ( 4.00 times 10^{8} N / m^{2}, ) the steel reptures. Determine. the shearing force necessary to (a) shear a steel bolt ( 1.00 mathrm{cm} ) in diameter and
(b) punch a
1.00-cm-diameter hole in a steel plate ( 0.500 mathrm{cm} ) thick.
11
655The length of an iron wire is ( L ) and area
of cross-section is ( A ). The increase in
length is ( l ) on applying the force ( F ) on its two ends. Which of the statement is
correct?
A. Increase in length is inversely proportional to its length
B. Increase in length is proportional to area of crosssection
C. Increase in length is inversely proportional to area of cross-section
D. Increase in length is proportional to Young’s modulus
11
656A point object is placed at a distance of
( 12 c m ) on the principal axis of a convex lens of focal length ( 10 mathrm{cm} ). A convex mirror is placed coaxially on the other side of the lens at a distance of ( 10 mathrm{cm} ). If
the final image coincides with the object, sketch the ray diagram and find the focal length of the convex mirror.
11
657A solid sphere of radius ( R ) and density ( rho ) is attached to one end of a mass-less
spring of force constant ( k . ) The other end of the spring is connected to another solid sphere of radius ( boldsymbol{R} ) and density ( mathbf{3} boldsymbol{rho} ) The complete arrangement is placed in
a liquid of density ( 2 rho ) and is allowed to
reach equilibrium. The correct
statement(s) is (are)

This question has multiple correct options
A ( cdot ) the net elongation of the spring is ( frac{4 pi R^{3} rho g}{3 k} )
B. the net elongation of the spring is ( frac{8 pi R^{3} rho g}{3 k} )
c. the light sphere is partially submerged
D. the light sphere is completely submerged

11
658Pressure applied on a rubber ball reduces the ball’s radius by ( 1 % ), what is the percentage volume strain of the ball
A . 1%
B. 3%
c. ( 5 % )
D. 0.5%
11
659Define Bulk modulus.11
660A material has Poisson’s ratio 0.3 .ff a
uniform rod of its suffers a longitudinal
strain of ( 3 times 10^{-3}, ) what will be the
percentage increase in volume?
11
661An aluminium rod (Young’s modulus ( = ) ( left.mathbf{7} times mathbf{1 0}^{mathbf{9}} mathbf{N} / mathbf{m}^{mathbf{2}}right) ) has a breaking strain of
( 0.2 % . ) The minimum cross-sectional
area of the rod in order to support a load
of ( 10^{4} ) Newton’s is:
( mathbf{A} cdot 1 times 10^{-2} m^{2} )
B. ( 1.4 times 10^{-3} m^{2} )
( mathrm{c} cdot 3.5 times 10^{-3} mathrm{m}^{2} )
D. ( 7.1 times 10^{-4} m^{2} )
11
662A wire of length 5 m is twisted through
( 30^{circ} ) at the free end. If the radius of wire
is 1 m ( m ), the shearing strain in the wire
is:
( A cdot 30 )
B . ( 0.36^{prime} )
( c cdot 1^{c} )
D. 0.18
11
663When the load applied to a suspended wire is increased from 3 kg-wt to 5 kgwt; the elongation increases from 0.6 ( mathrm{mm} ) to ( 1 mathrm{mm} . ) How much work is done
during the extention of the wire.
11
664A ball falling in a lake of depth ( 200 mathrm{m} ) show ( 0.1 % ) decrease in its volume at the
bottom. What is the bulk modulus of the
material of the ball:-
A ( cdot 19.6 times 10^{8} N / m^{2} )
B . ( 19.6 times 10^{-10} mathrm{N} / mathrm{m}^{2} )
C. ( 19.6 times 10^{10} N / m^{2} )
D. ( 19.6 times 10^{-8} N / m^{2} )
11
665In the spring-ball model of intermolecular forces, the balls
represent ( _{text {一一一一一一 }} ) and springs
represent
A. atoms, inter atomic forces
B. nuclei, nuclear forces
c. masses, gravitational forces
D. none of the above
11
666Two wires of different material and
radius have their length in ratio of 1: 2
if these were stretched by the same force, the strain produced will be in the
ratio.
A . 4: 1
B. 1: 1
c. 2: 1
D. 1: 2
11
667One end of uniform wire of length ( L ) and of weight ( W ) is attached rigidly to a
point in the roof and a weight ( W_{1} ) is
suspended from the lower end. If ( boldsymbol{A} ) is
the area of cross-section of the wire, the
stress in the wire at a height ( frac{3 L}{4} ) from its lower end is:
A. ( frac{W_{1}}{A} )
( ^{text {В } cdot} frac{left(W_{1}+frac{W}{4}right)}{A} )
( frac{left(W_{1}+frac{3 W}{4}right)}{A} )
D. ( frac{W_{1}+W}{A} )
11
668The slope of a Normal stress vs Linear
strain in the linear region of the graph for a copper wire gives us
A. Young’s modulus
B. Rigidity modulus
c. Bulk’s modulus
D. Poisson’s ratio
11
669When a ( 4 k g ) mass is hung vertically on a light spring that obeys Hooke’s law,
the spring stretches by 2 cms. The work required to be done by an external agent in stretching this spring by ( 5 c m s ) will
be ( left(boldsymbol{g}=mathbf{9 . 8 m} / boldsymbol{s e c}^{2}right) )
A. 4.900 joule
B . 2.450 joule
c. 0.495 joule
D. 0.245 joule
11
670Assertion
Strain is a unitless quantity.
Reason

Strain is equivalent to force
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
671In determination of young modulus of elasticity of wire, a force is applied and extension is recorded. Initial length of
wire is ( 1 mathrm{m} ). The curve between
extension and stress is depicted then young modulus of wire will be:
11
672Calculate the torque ( N ) twisting a stee tube of length ( l=3.0 m ) through an
angle ( varphi=2.0^{circ} ) about its axis, if the
inside and outside diameters of the
tube are equal to ( d_{1}=30 m m ) and
( boldsymbol{d}_{2}=mathbf{5 0} boldsymbol{m} boldsymbol{m} )
11
673A long rod of radius ( 1 mathrm{cm} ) and length ( 2 mathrm{m} ) which is fixed at one end is given a twist of 0.8 radian. The shear strain
developed will be :
A. 0.001 radians
B. 0.004 radians
c. 0.002 radians
D. 0.04 radians
11
674For which material the poisson’s ratio is greater than 1
A. steel
B. Copper
c. Aluminium
D. None of the above
11
675( (Delta l) ) of a wire of length ( 1 mathrm{m} ) suspended
from the top of a . roof at one end and
with a load W connected to the other
end. If the cross-sectional area of the
wire is ( 10^{-6} m^{2}, ) calculate the Young’s
modulus of the material of the wire.
A ( cdot 2 times 10^{11} N / m^{2} )
B . ( 2 times 10^{-11} N / m^{2} )
( mathbf{C} cdot 3 times 10^{-12} N / m^{2} )
D ( cdot 2 times 10^{-13} N / m^{2} )
11
676The Bulk modulus for an
incompressible liquid is :
A. zero
B. Unity
c. Infinty
D. Between O and 1
11
677In Searle’s experiment to find Young’s modulus the diameter of wire is
measured as ( boldsymbol{d}=mathbf{0 . 0 5 c m}, ) length of
wire is ( l=125 c m ) and when a weight,
( boldsymbol{m}=mathbf{2 0 . 0 k g} ) is put, extension in wire
was found to be ( 0.100 mathrm{cm} ). Find the
maximum permissible error in Young’s modulus ( (Y) . ) Use: ( Y=frac{m g l}{(pi / 4) d^{2} x} )
A . ( 6.3 % )
в. ( 5.3 % )
( c .2 .3 % )
D. 1%
11
678The formula relating youngs modulus
(Y), rigidity modulus (n) and Poisson’s ratio ( (sigma) ) is
( mathbf{A} cdot Y=2 n(1-sigma) )
В . ( Y=2 n(1+sigma) )
c. ( Y=n(1-2 sigma) )
D. ( Y=n(1+2 sigma) )
11
679One end of a steel (density ( p ) ) rectangular girder is embedded into a wall (fig). Due to gravity it sags slightly. Find the radius of curvature of the
neutral layer in the vicinity of the point O if the length of the protruding section of the girder is equal to ( l=6.0 mathrm{cm} ) and
the thickness of the girder equals ( h= )
( mathbf{1 0} mathrm{cm} )
( ^{mathrm{A}} cdot_{R}=frac{h^{2} E}{p l^{2} g} )
B. ( quad R=frac{h^{2} E}{6 p l^{2} g} )
c. ( _{R}=frac{h^{2} E}{3 p l^{2} g} )
D. ( R=frac{h^{2} E}{7 p l^{2} g} )
11
680Proof resilience is related to
A. PE stored in an elastic body
B. stiffness of a beam
C . elastic fatigue
D. elastic relaxation
11
681Diagram shows stress-strain graph for two material A & B. The graphs are
drawn to scale.

The ratio of young modulli of ( A ) to
material B is

11
682A steel cylindrical rod of length ( l ) and
radius ( r ) is suspended by its end from
the ceiling. Define ( U ) in terms of tensile
( operatorname{strain} frac{Delta l}{l} ) of the rod
A ( quad U=frac{2}{3} pi r^{2} l Eleft(frac{Delta l}{l}right)^{2} )
в. ( U=frac{4}{3} pi r^{3} l Eleft(frac{Delta l}{l}right)^{3} )
( ^{mathrm{c}} cdot u=frac{2}{4} pi r^{3} l Eleft(frac{Delta l}{l}right)^{2} )
D. None of these
11
683The maximum strain energy that can be stored in a body is known as:
A. impact energy
B. toughness
c. proof resilience
D. none of the above
11
684The Marina trench is located in the
Pacific Ocean, and at one place it is nearly eleven km beneath the surface of
water. The water pressure at the bottom
of the trench is about ( 1.1 times 10^{8} ) Pa.
steel ball of initial volume ( 0.32 m^{3} ) is
dropped into the ocean and falls to the bottom of the trench. What is the
change in the volume of the ball when it reaches to the bottom?
11
685Scalar are quantity that are describe by
A. Direction
B. Magnitude and direction
c. Magnitude
D. Motion
11
686A steel bolt is inserted into a copper
tube as shown in figure. Find the forces induced in the bolt and in the tube when
the nut is turned through one revolution. Assume that the length of the tube is ( l ), the pitch of the bolt thread
is ( h ) and the cross-sectional areas of the
steel bolt and the copper tube are ( boldsymbol{A}_{s} )
and ( A_{c}, ) respectively
11
687A light rod of length ( 2 m ) is suspended
from the ceiling horizontally by means
of two vertical wires of equal length tied to its ends. One of the wires is made of
steel and is of cross section ( 0.1 mathrm{cm}^{2} . ) A
weight is suspended from a certain
point of the rod such that equal stress are produced in both the wires.Which of the following are correct?
This question has multiple correct options
A. The ratio of tension in the steel and brass wires is 0.5
B. The load is suspended at a distance of ( 400 / 3 c m ) from the steel wire
c. Both (a) and
(b) are correct
D. Neither
(a) nor
(b) are correct
11
688The Hooke’s law defines
A. modulus of elasticity
B. stress
C. strain
D. elastic limit
11
689If the material has breaking point lies very close to elastic limit, the material
is
A. brittle
B. ductile
c. elastomer
D. diathermanous
11
690The force that must be applied to a steel wire ( 6 m ) long and diameter ( 1.6 m m ) to produce an extension of ( 1 mathrm{mm}[boldsymbol{y}= ) ( left.2.0 times 10^{11} N . m^{-2}right] ) is approximate.
A. ( 100 N )
в. ( 50 N )
( c .67 N )
D. 33.5N
11
691If a rubber ball is taken at the depth of ( 200 mathrm{m} ) in a pool its volume decreases by
( 0.1 % ) If the density of the water is ( 1 times ) ( 10^{3} k g / m^{3} ) and ( g=10 m / s^{2} ) then the
volume elasticity in ( N / m^{2} ) will be
A ( cdot 10^{8} )
в. ( 2 times 10^{8} )
( c cdot 10^{9} )
D. ( 2 times 10^{9} )
11
692The Poisson’s ratio of a material is ( 0.5 . ) If
a force is applied to a wire of this material, there is a decrease in the
cross-sectional area by ( 4 % ). The percentage increase in the length is:
A . ( 1 % )
B. 2%
( c .2 .5 % )
D. ( 4 % )
11
693When an elastic material with Young’s
modulus ( ^{prime} Y^{prime} ) is subjected to a
stretching stress ( ^{prime} S^{prime}, ) then the elastic
energy stored per unit volume is:
( ^{A} cdot frac{S^{2}}{2 Y} )
B. ( frac{Y S^{2}}{2} )
c. ( frac{s}{2 Y} )
D. ( frac{Y S}{2} )
11
694An increase in pressure required to decreases the 100 liters volume of a
liquid by ( 0.004 % ) in container is:
(Bulk modulus of the liquid ( = )
( 2100 M P a) )
A. ( 188 k P a )
в. ( 8.4 k P a )
c. ( 18.8 k P a )
D. ( 84 k P a )
11
695A spiral spring is stretched to ( 20.5 mathrm{cm} ) gradation on a metre scale when loaded with a 100 g load and to the ( 23.3 mathrm{cm} ) gradation by 200 g load. The spring is used to support a lump of metal in air and the reading now is ( 24.0 mathrm{cm} . ) The mass of metal lump is :
A. 250gm
в. 225 gm
c. ( 145 mathrm{gm} )
D. 750 gm
11
696A uniform rod of length ( ^{prime} L^{prime} ) and density
( rho^{prime} ) is being pulled along a smooth floor
with horizontal acceleration ( alpha ) as shown
in the figure. The magnitude of the stress at the transverse cross-section
through the mid-point of the rod is
A ( frac{rho l alpha}{4} )
в. ( 4 rho l ) d
( c cdot 2 rho l )
D. ( frac{rho l alpha}{2} )
11
697A bob of mass ( m ) hangs from the ceiling
of a smooth trolley car which is moving
with a constant acceleration ( a ). If the
Young’s modulus, radius and length of
the string are ( Y, r ) and ( l ) respectively
f the stress in the string is ( frac{2 m sqrt{g^{2}+d^{2}}}{x pi r^{2}} . ) Find ( x )
11
698Three elastic wires, ( P Q, P R ) and ( P S )
support a body ( P ) of mass ( M, ) as shown
in the figure. The wires. are of the same
material and cross-sectional area, the
middle one being vertical. The load carried by the middle wire is:
A ( cdot frac{M g}{1+2 cos ^{2} theta} )
в. ( frac{M g}{1+2 cos ^{3} theta} )
( c )
D. ( frac{M g}{cos theta+2 cos ^{3} theta} )
11
699A thin ( 1 mathrm{m} ) long rod has a radius of 5
mm.1 A force of 50 ( pi k N ) is applied at
one end to determine its Young’s modulus. Assume that the force is
exactly known. If the least count in the measurement of all lengths is ( 0.01 mathrm{mm} ) which of the following statements is false?
A. The maximum value of ( Y ) that can be determined is ( 10^{14} N / m^{2} )
B. ( frac{Delta Y}{Y} ) gets minimum contribution. from the uncertainty in the length.
c. ( frac{Delta Y}{Y} ) gets its maximum contribution from the uncertainty in strain
D. The figure of merit is the largest for the length of the rod
11
700A uniform wire of length ( 4 m ) and area of
( operatorname{cross} operatorname{section} 2 m m^{2} ) is subjected to
longitudinal force produced an
elongation of 1 mm.lf ( Y=0.2 times 10^{11} mathrm{NM}^{-2} )
elastic potential energy stored in the body is
A. ( 0.5 J )
( J )
в. ( 0.05 J )
c. ( 0.005 J )
D. ( 5.0 J )
11
701A uniform metal rod of ( 2 m m^{2} ) cross
section is heated from ( 0^{circ} mathrm{C} ) to ( 20^{circ} mathrm{C} ). The
coefficient of linear expansion of the rod is ( 12 times 10^{-6 / 0} mathrm{C} ). Its Young’s modulus of
elasticity is ( 10^{11} mathrm{N} / mathrm{m}^{2} ). The
energy stored per unit volume of the rod
is :
( mathbf{A} cdot 2880 J / m^{3} )
B . ( 1500 J / m^{3} )
c. ( 5760 J / m^{3} )
D. ( 1440 J / m^{3} )
11
702The density of a metal at normal
pressure is ( rho . ) It’s density when it is
subjected to an excess pressure p is ( rho ) ‘.
If ( mathrm{B} ) is the bulk modulus of the metal,
the ratio ( rho^{prime} / rho ) is :
A. ( frac{1}{1-p / B} )
в. ( 1+frac{P}{B} )
c. ( frac{1}{1-B / p} )
D. ( 1+B / p )
11
703The breaking stress of aluminium is
( mathbf{7} . mathbf{5} times mathbf{1 0}^{7} mathbf{N m}^{-2} . ) The greatest length of
aluminium wire that can hang vertically without breaking is
(Density of aluminium is ( 2.7 times ) ( left.10^{3} k g m^{-3}right) )
A ( cdot 283 times 10^{3} m )
В. ( 28.3 times 10^{3} m )
c. ( 2.72 times 10^{3} m )
D. ( 0.283 times 10^{3} m )
11
704A solid cube is subjected to a pressure
of ( left(5 times 10^{5} quad N / m^{2}right) . ) Each side of the
cube is shortened by then volumetric strain and Bulk modulus of the cube are
( begin{array}{ll}text { A. } 0.03,5 times 10^{5} & text { N } / m^{2}end{array} )
B. ( 0.03,1.67 times 10^{7} quad N / m^{2} )
C. ( 3,1.67 times 10^{-7} quad N / m^{2} )
D. ( 0.01,1.67 times 10^{7} quad N / m^{2} )
11
705A copper wire of negligible mass, ( 1 m )
length and cross-sectional area ( 10^{-6} m^{2} )
is kept on a smooth horizontal table
with one end fixed. A ball of mass ( 1 k g ) is
attached to the other end. The wire and
the ball are rotating with an angular velocity of 20 rad/s. If the elongation in the wire is ( 10^{-3} m . ) Find the Young’s
modulus of the wire (in terms of
( mathbf{1 0}^{11} mathbf{N} / boldsymbol{m}^{2} mathbf{)} )
11
706If the ratio of lengths, radii and Young’s modulus of steel and brass wires shown
in the figure are ( a, b ) and ( c ) respectively, the ratio between the increase in
lengths of brass and steel wires would
be :
A ( cdot frac{b^{2}}{2 c} )
в. ( frac{b c}{2 a^{2}} )
( c cdot frac{b a^{2}}{2 c} )
D. ( frac{2 b^{2} c}{a} )
11
707A uniform wire of Youngs modulus Y is stretched by a force within the elastic limit. If ( S ) is the stress produced in the
wire and ( varepsilon ) is the strain in it, the
potential energy stored per unit volume is given by
This question has multiple correct options
A ( cdot frac{1}{2} varepsilon S )
в. ( frac{1}{2} Y varepsilon^{2} )
c. ( frac{s^{2}}{2 Y} )
D. ( frac{1}{2} Y varepsilon S )
11
708A copper wire 4 m long has diameter of
1 ( m m ), if a load of ( 10 k g ) wt is attached
at other end. What extension is
produced, if Poisson’s ratio is ( 0.26 ? ) How much lateral compression is produced in it? ( left(boldsymbol{Y}_{boldsymbol{c u}}=mathbf{1 2 . 5} times mathbf{1 0}^{mathbf{1 0}} boldsymbol{N} / boldsymbol{m}^{2}right) )
11
709A rod ( 100 mathrm{cm} ) long and of ( 2 mathrm{cm} times 2 mathrm{cm} )
cross-section is subjected to a pull of 1000kg force. Modulus of elasticity of
the material is ( 2.0 times 10^{6} k g / c m^{2} . ) If the
elongation of the rod is ( x mathrm{mm} ), find the
value of ( 40 x )
11
710A material has Poisson’s ratio 0.5 . if a
uniform rod of it suffers a longitudinal
strain of ( 2 times 10^{3}, ) then the percentage
change in volume is
A . 0.6
B. 0.4
( c .0 .2 )
D. zero
11
711A cube is shifted to a depth of ( 100 m ) is
alake. The change in volume is ( 0.1 % ). The bulk modules of the material is nearly
( mathbf{A} cdot 10 P a )
в. ( 10^{4} P a )
( mathbf{c} cdot 10^{7} P a )
D. ( 10^{9} mathrm{Pa} )
11
712A metal cube of side length ( 8.0 mathrm{cm} ) has its upper surface displaced with
respect to the bottom by ( 0.10 mathrm{mm} ) when a tangential force of ( 4 times N ) is applied at the top with bottom surface fixed. The
rigidity modulus of the material of the
cube is
A ( cdot 4 times 10^{14} N / m^{2} )
B . ( 5 times 10^{9} mathrm{N} / mathrm{m}^{2} )
c. ( 8 times 10^{14} mathrm{N} / mathrm{m}^{2} )
D. ( 1 times 10^{14} mathrm{N} / mathrm{m}^{2} )
11
713The Sl unit of stress is same as the SI
unit of
A. Strain
B. Modulus of elasticity
c. Pressure
D. Both (2) and (3)
11
714If longitudinal strain for a wire is 0.03
and its poisson ratio is ( 0.5, ) then its lateral strain is
( mathbf{A} cdot 0.003 )
в. 0.0075
c. 0.015
D. 0.4
11
715The hardest material out of the
following is :
A. diamond
B. steel
c. aluminium
D. glass
11
716A load of ( 4.0 mathrm{kg} ) is suspended from a ceiling through a steel wire of length ( 20 m ) and radius ( 2.0 m m . ) It is found
that the length of the wire increases by
( 0.031 m m ) as equilibrium is achieved. If
( boldsymbol{g}=mathbf{3 . 1} boldsymbol{x} boldsymbol{pi} boldsymbol{m} boldsymbol{s}^{-2}, ) the value of young’s
modulus in ( N m^{-2} ) is
( mathbf{A} cdot 2.0 times 10^{12} )
B . ( 4.0 times 10^{11} )
( mathbf{c} cdot 2.0 times 10^{11} )
D. ( 0.02 times 10^{9} )
11
717A student performs an experiment to determine the Young’s modulus of a
wire, exactly ( 2 m ) long, by Searle’s method. In a particular reading, the student measures the extension in the
length of the wire to be ( 0.8 m m ) with an
uncertainty of ( 0.05 m m ) at a load of
exactly ( 1.0 mathrm{kg} ). The student also
measures the diameter of the wire to be
( 0.4 m m ) with an uncertainty of ( 0.01 m m . ) Take ( g=9.8 m s^{-2}(text {exact }) )
The Young’s modulus obtained from the reading is
A ( cdot(2.0 pm 0.3) times 10^{11} N m^{-2} )
в. ( (2.0 pm 0.2) times 10^{11} mathrm{Nm}^{-2} )
c. ( (2.0 pm 0.1) times 10^{11} mathrm{Nm}^{-2} )
D. ( (2.0 pm 0.05) times 10^{11} mathrm{Nm}^{-2} )
11
718A fixed volume of iron is drawn into a wire of length ( 1 . ) The extension produced in this wire by a constant force F is proportional to then:-
A ( cdot frac{1}{l^{2}} )
B. ( frac{1}{l} )
( c cdot l^{2} )
( D )
11
719An elastic metal rod will change its
length when it
This question has multiple correct options
A. falls vertically under its weight
B. is pulled along its length by a force acting at one end
c. rotates about an axis at one end
D. slides on a rough surface
11
720A copper wire of length ( 2.2 mathrm{m} ) and a steel wire of length ( 1.6 mathrm{m}, ) both of diameter 3.0 ( mathrm{mm} ) are connected end to end. When
stretched by a force, the elonation in length ( 0.50 mathrm{mm} ) is produced in the copper wire. The stretching force is ( left(Y_{c u}=1.1 times 10^{11} N / m^{2}, Y_{text {steel}}=2.0 timesright. )
( left.mathbf{1 0}^{mathbf{1 1}} mathbf{N} / boldsymbol{m}^{mathbf{2}}right) )
A ( cdot 5.4 times 10^{2} N )
B . ( 3.6 times 10^{2} N )
c. ( 2.4 times 10^{2} N )
D. ( 1.8 times 10^{2} N )
11
721( A ) and ( B ) are two wires. The radius of ( A )
is twice that of ( B ). They are stretched by
the same load. Then the stress on ( B ) is
A. equal to that on ( A )
B. four times that on ( A )
c. two times that on ( A )
D. half that on ( A )
11
722Find the fractional decrement of its
volume
A ( cdot frac{Delta V}{V}=-frac{3 p}{E}(1-2 mu) )
B. ( frac{Delta V}{V}=-frac{3 p}{E}(1+2 mu) )
c. ( frac{Delta V}{V}=frac{2 p}{E}(1+3 mu) )
D. None of these
11
723As shown in the figure, force of ( 105 N )
each are applied in opposite directions,
on the upper and lower force of a cube of
side ( 10 mathrm{cm}, ) shifting the upper face
parallel to itself by ( 0.5 mathrm{cm} . ) If the side of
another cube of the same material is
( 20 mathrm{cm}, ) then under similar condition as
shown as above, the displacement will
be:
( mathbf{A} cdot 0.25 mathrm{cm} )
B. ( 0.37 mathrm{cm} )
c. ( 0.75 mathrm{cm} )
D. ( 1.00 mathrm{cm} )
11
724Young modulus of elasticity of brass is ( 10^{11} N / m^{2} . ) The increase in its energy
on pressing a rod of length ( 0.1 m ) and
cross-sectional area ( 1 mathrm{cm}^{2} ) made of
brass with a force of ( 10 mathrm{kg} ) along its
length,will be ( x times 10^{-7} ). Find ( x )
11
725What is plastic?11
726Two wires ( A ) and ( B ) of same dimensions
are stretched by same amount of force. Young’s modulus of ( A ) is twice that of ( B ).
Which wire will get more elongation? Enter 1 for ( A ) and 2 for ( B )
11
727A uniform steel rod of ( 5 m m^{2} ) cross
section is heated from ( 0^{circ} C ) to ( 25^{circ} C . )
Calculate the force which must be
exerted to prevent it from expanding.
Also calculate strain.
(a for steel ( =12 times 10^{-6} /^{circ} mathrm{C} ) and ( gamma ) for
steel ( left.=20 times 10^{10} N / m^{2}right) )
11
728The length of a wire under stress changes by ( 0.01 % . ) The strain produced is
( mathbf{A} cdot 1 times 10^{-4} )
B. 0.01
( c )
D. ( 10^{4} )
11
729The elongation produced in a copper wire of length ( 2 mathrm{m} ) and diameter ( 3 mathrm{mm} ) when a force of ( 30 mathrm{N} ) is applied is ( [mathrm{Y}= ) ( left.1 times 10^{11} mathrm{N} cdot mathrm{m}^{-2}right] )
A. ( 8.5 m m )
B. ( 0.85 mathrm{mm} )
c. ( 0.085 m m )
D. ( 85 m m )
11
730A weightless rod is acted on by upward parallel forces of ( 2 N ) and ( 4 N ) ends ( A )
and ( B ) respectively.; The total length of
the rod ( A B=3 m . ) To keep the rod in
equilibrium a force of ( 6 N ) should act in
the following manner.
A. Downwards at any point between ( A ) and ( B ).
B. Downwards at mid point of ( A B ).
c. Downwards at a point ( C ) such that ( A C=1 m ).
D. Downwards at a point ( D ) such that ( B D=1 m ).
11
731Three blocks, each of same mass ( m )
are connected with wire ( W_{1} ) and ( W_{2} ) of
same cross sectional area ‘a’ and

Young’s modulus Y. Neglecting friction,
the strain developed in wire ( W_{2} ) is
A ( frac{2 m g}{3} frac{m g}{a Y} )
в. ( frac{3}{2} frac{m g}{a Y} )
( c )
( D )

11
732According to Hooke’s law of elasticity, if stress is increased, the ratio of stress to
strain
A . decreases
B. increases
c. becomes zero
D. remains constant
11
733A wire is stretched through 1 mm by certain load. The extension produced in the wire of same material with double
the length and radius will be
( mathbf{A} cdot 4 m m )
B. ( 3 m m )
( mathbf{c} cdot 1 m m )
D. ( 0.5 m m )
11
734The length of a wire is 4 m. Its length is
increased by ( 2 m m ) when a force acts on
it. The strain is:
A. ( 0.5 times 10^{-3} )
B. ( 5 times 10^{-3} )
( c cdot 2 times 10^{-3} )
D. 0.05
11
735When a certain force is applied on a
string it extends by ( 0.01 mathrm{cm} . ) When the same force is applied on another string of same material, twice the length and double the diameter, then the extension
in second string is
( A cdot 0.005 mathrm{cm} )
B. 0.02 cm
c. ( 0.08 mathrm{cm} )
D. ( 0.04 mathrm{cm} )
11
736A thin uniform metallic rod of mass ( M )
and length ( L ) is rotated with a angular
velocity ( omega ) in a horizontal plane about a
vertical axis passing through one of its ends. The tension in the middle of the
rod is :
A ( cdot frac{1}{2} M L omega^{2} )
B ( cdot frac{1}{4} M L omega^{2} )
c. ( frac{1}{8} M L omega^{2} )
D. ( frac{3}{8} M L omega^{2} )
11
737The radii and Young’s moduli of two
uniform wires ( A ) and ( B ) are in the ratio
2: 1 and 1: 2 respectively. Both wires are subjected to the same longitudinal force. If the increase in length of the wire ( A ) is one percent, the percentage
increase in length of the wire ( B ) is:
A . 1.0
в. 1.5
( c .2 .0 )
D. 3.0
11
738For a given material, the Young’s modulus is 2.4 times that of the
modulus of rigidity. Its Poisson’s ratio is
A . 2.4
B. 1.2
( c .0 .4 )
D. 0.2
11
739There is no change in volume of a wire due to change in its length of stretching. The Poisson’s ratio of the material of the wire is:
A . 0.50
B . – 0.50
( c cdot 0.25 )
D . – 0.25
11
740The Y of a material having a cross sectional area of ( 1 mathrm{cm}^{2} ) is ( 2 times 10^{12} )
dynes/cm ( ^{2} ). The force required to double the length of the wire is:
A ( cdot 1 times 10^{12} ) dynes
B. 2 x 10 ( ^{12} ) dynes
c. ( 0.5 times 10^{12} ) dynes
D. ( 4 times 10^{12} ) dynes
11
741A force of ( 10 mathrm{N} ) is applied to an object,
whose area is ( 5 mathrm{cm}^{2} ) at an angle of 30
degrees with the vertical. What kind of stress can be found from this data
A. Normal and areal stress can be found
B. only normal stress can be found
c. only areal stress can be found
D. Stress cannot be found from this data, since applied force is neither along the horizontal or vertica
11
742A rod is made of uniform material and
has non-uniform cross-section. It is
fixed at both ends as shown and heated
at the mid-section. Which of the
following statements are not correct?
his question has multiple correct options
A. Force of compression in the rod will be maximum at mid-section
B. Compressive stress in the rod will be maximum at left end
c. since the rod is fixed at both the ends, its length will remain unchanged. Hence, no strain will be induced in it.
D. None of above
11
743What is the tension in string at ( A ) immediately after the string at ( mathrm{B} )
breaks?
A ( cdot frac{m g}{5} )
в. ( frac{2 m g}{31} )
c. ( frac{m g}{37} )
D. ( frac{5 m g}{37} )
11
744Assertion ( (A): ) Bulk modulus of
elasticity (K) represents
incompressibility of the material.
Reason ( (mathrm{R}): K=-frac{Delta P}{Delta V / V}, ) where
symbols have their standard meaning.
A. Both assertion and reason are true and the reason is
correct explanation of the assertion
B. Both assertion and reason are true, but reason is not correct explanation of the assertion
C. Assertion is true, but the reason is false
D. Assertion is false, but the reason is true
11
745Column
(order of magnitude in Pa)
11
746Assertion
If we apply force to a lump of putty or mud, they have no gross tendency to regain their previous shape.
Reason
This type of substances are called
plastic substances.
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
747Two wires ( A ) and ( B ) of radius ( 2 r ) and ( r )
respectively are joined and a force ( boldsymbol{F} ) is
applied at the end. The length of each
wire is ( L . ) Their Youngs modulus are ( Y )
and ( 2 Y ) respectively. Find the net elongation.
11
748Determine the value of ( x ) so that equal
strains are produced in each wire.
( A cdot 1 )
( 3.2 m )
( c .3 m )
D. 2.2 n
11
749( frac{E}{L} )11
750A ( 2 m m^{2} ) cross-sectional area wire is
stretched by ( 4 mathrm{mm} ) by a certain weight.If
the same material wire of cross-
sectional area ( 8 m m^{2} ) is stretched by
the same weight, the stretched length
is
( A cdot 2 m m )
B. ( 0.5 mathrm{mm} )
( mathrm{c} cdot 1 mathrm{mm} )
D. ( 1.5 mathrm{mm} )
11
751Assertion
The maximum height of a mountain on earth can be estimated from the elastic
behaviour of rocks.
Reason
At the base of mountain, the pressure is less than elastic limit of earth’s
supporting material
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
752Nature of shear stress is
A. Positive
B. Negative
C. Positive as well as negative
D. Is always less than 0.5
11
753The property of metals which allows them to be drawn into wires is known as
A. ductility
B. malleability
c. elasticity
D. compressibility
11
754Shear modulus is zero for
A. Solids
B. Liquids
c. Gases
D. Liquids and gases
11
755Two parallel and opposite forces each ( mathbf{5 0 0 0} N ) are applied tangentially to the upper and lower faces of a cubical
metal block of side ( 25 mathrm{cm} . ) The angle of
shear is then
(The shear modulus of the metal is
( 80 G P a) )
A ( cdot 10^{-4} x a d )
B ( cdot 10^{-5} r a d )
c. ( 10^{-6} )rad
D. ( 10^{-7} r a d )
11
756The load versus strain graph for four
wires of the same material is shown in
the figure. The thickest wire is
represented by the line
( A cdot O B )
в. ( O A )
( c cdot O D )
D. ( O C )
11
757What is Plasticity?11
758The length of a rubber cord is ( l_{1} ) when
the tension is ( 4 N ) and ( l_{2} m ) when the
tension is ( 6 N . ) The length when the
tension is ( 9 N, ) is:
A ( cdotleft(2.5 l_{2}-1.5 l_{1}right) m )
В ( cdotleft(6 l_{2}-1.5 l_{1}right) m )
c. ( left(3 l_{2}-2 l_{1}right) m )
D・ ( left(3.5 l_{2}-2.5 l_{1}right) m )
11
759Fill in the blank.
In a technical sense a substance with a
elasticity is one that requires a force to
produce a distortion-for example, a steel sphere.
A. high, small
B. high, large
c. low, large
D. low, small
11
760(i) For a Searle’s experiment, in the
graph shown, there are two readings a
and b that are not lying on the straight
line
(ii) Experiment is not performed
precisely
A. Both (i) and (ii) are true and (ii) is reason for (i)
B. Both (i) and (ii) are true but (ii) is not reason for (ii)
c. only (i) is true
D. only (ii) is true
11
761Q Type your question
following statements:
It will be easier to compress this
rubber then expand it
II. Rubber does not return to its
original length after it is stretched
III. The rubber band will get heated if it
is stretched and released.

Which of these can be deduced from the
graph?
A. III only
B. II and III
c. ( I ) and ( I I I )
D. I only

11
762A uniform steel wire of length ( 3 m ) and
are of cross section ( 2 m m^{2} ) is extended
through ( 3 m m ) Calculate the energy
stored in the wire, if the elastic limit is
not exceeded
11
763The breaking stress of aluminium is ( mathbf{7 . 5} times mathbf{1 0}^{7} mathbf{N m}^{-mathbf{2}} . ) Find the greatest
length of aluminium wire that can hang vertically without breaking. Density of aluminium is ( 2.7 times 10^{3} mathrm{Kgm}^{-3} )
11
764Two wires are made of the same
material and have the same volume.
However wire 1 has cross-sectional area
( A ) and wire 2 has cross- sectional area
3 A. If the length of wire 1 increases by ( Delta x ) on applying force ( F, ) how much force is needed to stretch wire 2 by the same
amount ?
A.
B. 4 F
( c .6 mathrm{F} )
D. 9 F
11
765A copper wire is held at the two ends
between two rigid supports. At ( 30^{circ} mathrm{C} ) the wire is just taut,with negligible tension. If ( boldsymbol{Y}=mathbf{1 3} times mathbf{1 0}^{mathbf{1 1}} mathbf{N m}^{-mathbf{2}}, boldsymbol{alpha}= )
( 1.7 times 10^{-5}left(^{circ} Cright)^{-1} ) and density ( rho=9 times )
( 10^{3} k g m^{-3}, ) then the speed of
transverse wave in this wire at ( 10^{circ} mathrm{C} ) is:
A ( cdot 90 m s^{-1} )
B. ( 70 m s^{-1} )
( mathrm{c} cdot 60 mathrm{ms}^{-1} )
D. ( 100 mathrm{ms}^{-1} )
11
766A Toy cart attached to the end of an
unstretched string of length a, when received moves on a smooth horizontal
table in a circle of radius 2 s with a time
period T. Now the toy cart is speeded up until it moves in a circle of radius 3 a
with a period ‘T’. If Hook’s law holds then (Assume no friction)
A ( cdot T^{prime}=sqrt{frac{3}{2}} pi )
B cdot ( T^{prime}=left(frac{sqrt{3}}{2}right) T )
( mathbf{c} cdot mathbf{T}^{prime}=left(frac{3}{2}right) mathbf{T} )
D. ( T^{prime}=T )
11
767Three wires ( A, B, C ) made of the same
material and radius have different
lengths. The graphs in the figure shows
the elongation-load variation. The
longest wire is:
( A )
B. B
( c cdot c )
D. Al
11
768An elastic spring is given a force of 1000
N over an area of ( 0.2 m^{2} )
A. ( 3000 N m^{-2} )
B. ( 5000 mathrm{Nm}^{-2} )
c. ( 500 N m^{-2} )
D. ( 2500 N m^{-2} )
11
769Assuming that shear stress of base of a mountain is equal to force per unit area to its weight, calculate the maximum possible height of a mountain on the earth if breaking stress of a typical rock
is ( 30 times 10^{7} N m^{-2} ) and specific gravity
is ( 3 times 10^{3} k g / m^{3} )
( A cdot 10 mathrm{km} )
B. ( 8 mathrm{km} )
( c cdot 7 k m )
( D .6 mathrm{km} )
11
770A helical spring is stretched by a force, the resultant strain produced in the spring is:
A. volume strain
B. shearing strain
c. longitudinal strain
D. all the above
11
771Young’s modulus of rubber is ( 10^{4} mathrm{N} / m^{2} )
and area of cross-section is ( 2 mathrm{cm}^{2} ). If
force of ( 2 times 10^{5} ) dyne is applied along
its length, then its final length becomes.
A . ( 3 L )
B. ( 4 L )
( c cdot 2 L )
D. None of these
11
772( mathbf{A} )
1.05 ( m ) having negligible mass is
supported at its ends by two wires
of steel (wire ( A ) ) and aluminium (wire ( B )
of equal lengths as shown in Fig. The cross-sectional areas of wires ( A ) and ( B )
are ( 1.0 m m^{2} ) and ( 2.0 m m^{2}, ) respectively
At what point along the rod should a
mass ( m ) be suspended in order
to produce
(a) Equal stress in ( A ) and ( B ) and
(b) Equal strains in ( A ) and ( B ) ?
11
773The Young’s modulus of the material of a wire of length L and radius r is ( Y )
newton per ( m^{2} ). If the length of the wire
is reduced to ( L / 2 ) and the radius to ( r / 2 ) then its Young’s modulus will be.
A. ( Y / 2 )
B.
( c .2 Y )
D. ( 4 Y )
11
774( 32 g ) of ( O_{2} ) is contained in a cubical
container of side ( 1 m ) and maintained
at a temperature of ( 127^{0} C . ) The isothermal bulk modulus of elasticity of
the gas in terms of universal gas constant ( boldsymbol{R} ) is
( mathbf{A} cdot 127 R )
B. ( 400 R )
( c cdot 200 R )
D. ( 560 R )
11
775A ( 5 m ) long cylindrical steel wire with
radius ( 2 times 10^{-3} mathrm{m} ) is suspended
vertically from a rigid support and carrics a bob of mass ( 100 mathrm{kg} ) at the
other end. If the bob gets snapped,
calculate the change in temperature of the wire ignoring radiation losses. ( left(text { Take } g=10 m / s^{2}right) ) (For the steel wire:
Young’s modulus ( =2.1 times 10^{11} N / m^{2} )
Density ( =7860 k g / m^{3} ) Specific heat ( = )
( 420 J / k g C) )
11
7767. A spring of force constant k is cut into two pieces such that
one piece is double the length of the other. Then the long
piece will have a force constant of (IIT JEE, 1999)
3
c. 3k
d. 6k
11
777Solids which break or rupture above the elastic limit are classified as:
A . brittle
B. elastic
c. ductile
D. malleable
11
778A material upon heavy stress undergoes a deformation and lands a part of permanent set. Upon removal of the stress, the material will
A. return to its original position
B. become permanently plastic
c. start oscillating about the elastic point
D. start oscillating about the yield point
11
779What should be done if the gas cylinder at your home catches fire?
A. Water should be sprinkled.
B. Sand, soil should be put at it.
c. cylinder should be covered with wet blanket.
D. One should run away
11
780A wire of length L and of cross-sectional area A is made of a material of Young’s modulus Y. The work done in stretching the wire by an amount ( x ) is given by :
A ( cdot frac{Y A x^{2}}{L} )
в. ( frac{Y A x^{2}}{2 L} )
c. ( frac{Y A L^{2}}{x} )
D. ( frac{Y A L^{2}}{2 x} )
11
781The correct relation between
interatomic force constant ( K, ) Young
modulus ( Y ) and interatomic distance ( r_{0} )
is
A. ( K=Y r_{0} )
в. ( K=frac{r_{0}}{Y} )
( c cdot K=frac{Y}{r_{0}} )
D. ( K=r_{0}^{2} Y^{2} )
11
782When a sphere of radius ( 2 mathrm{cm} ) is
suspended at the end of a wire,
elongation is ‘e’. When the same wire is loaded with a sphere of radius ( 3 mathrm{cm} ) and made of the same material,
the elongation would be :
A ( cdot frac{8}{27} e )
в. ( frac{27}{8} e )
c. ( frac{4}{9} e )
D. ( frac{9}{4} )
11
783Stretching of a rubber band results in
A. No change in potential energy
B. Zero value of potential energy
C. Increase in potential energy
D. Decrease in potential energy
11
784Determine the shear stress at the pipe
wall
A. ( 8 times 10^{-6} N / m^{2} )
B. ( 3.9 times 10^{-6} N / m^{2} )
c. ( 2.3 times 10^{-6} N / m^{2} )
D. ( 10.6 times 10^{-6} N / m^{2} )
11
785A uniform cylindrical wire is subjected to a longitudinal tensile stress of ( 5 times ) ( 10^{7} N / m^{2} . ) Young’s modulus of the
material of the wire is ( 2 times 10^{11} N / m^{2} )
The volume change in the wire is ( 0.02 % )
The fractional change in the radius is
A. ( 0.25 times 10^{-4} )
B. ( 0.5 times 10^{-4} )
c. ( 0.1 times 10^{-4} )
D. ( 1.5 times 10^{-4} )
11
786If a stretching force ( F 1 ) is applied on a
vertical metal wire then its length is ( L 1 )
and if force ( F 2 ) is applied on it then its
length becomes 1.2. The real length of
wire is?
11
787Young’s modulus of the material of a wire is ( Y ). If it is under a stress ( S ), the
energy stored per unit volume is given
by:
A ( cdot frac{1}{2} frac{S}{Y} )
в. ( frac{1}{2} frac{S^{2}}{Y} )
c. ( frac{1}{2} frac{s}{Y^{2}} )
D. ( frac{1}{2} frac{S^{2}}{Y^{2}} )
11
788One end of a string of length L and cross-sectional area A is fixed to a
support and the other end is fixed to a
bob of mass ( mathrm{m} ). The bob is revolved in a
horizontal circle of radius ( r, ) with an
angular velocity ( omega, ) such that the string
makes an angle ( theta ) with the vertical. The increase ( Delta L ) in length of the string is
A ( cdot frac{M L}{A Y} )
В. ( frac{M g L}{A Y cos theta} )
c. ( frac{M g L}{A Y sin theta} )
D. ( frac{M g L}{A Y} )
11
789A copper wire of cross-section A is under a tension ( mathrm{T} ). Find the decrease in
the cross-section area. Young’s
modulus is ( Y ) and Poisson’s ratio is ( sigma )
( ^{text {A }} cdot frac{sigma T}{2 A Y} )
в. ( frac{sigma T}{A Y} )
c. ( frac{2 sigma T}{A Y} )
D. ( frac{4 sigma T}{A Y} )
11
790A wire is stretched by a force ( F . ) If ( s ) is the strain developed and ( Y ) is Young’s modulus of material of wire, then work
done per unit volume is
A ( cdot frac{Y s^{2}}{2} )
B. ( frac{s^{2}}{2 Y} )
c. ( frac{1}{2} F s )
D. ( frac{Y}{2 s^{2}} )
11
791Q Type your question
of ( 0.7 m m ) diameter and suspended
vertically. The stone is now rotated in a horizontal plane at a rate such that wire
makes an angle of ( 85^{circ} ) with the vertical
( f Y=7 times 10^{10} mathrm{Nm}^{-2}, sin 85^{circ}=0.9962 )
and ( cos 85^{circ}=0.0872, ) the increase in
length of wire is
( A cdot 1.67 times 10^{-3} mathrm{m} )
B. ( 6.17 times 10^{-3} mathrm{m} )
C ( cdot 1.76 times 10^{-3} mathrm{m} )
D. 7.16×10-3 ( m )
11
792For perfectly rigid bodies, the elastic constants ( Y, B ) and ( n ) are
A. ( Y=B=n=0 )
B. ( Y=B=n ) -infinity
c. ( Y=2 B=3 n )
D. ( Y=B=n=0.5 )
11
793The expression for the determination of Poisson’s ratio for rubber is
A ( cdot sigma=frac{1}{2}left[1-frac{d V}{A d L}right] )
в. ( sigma=frac{1}{2}left[1+frac{d V}{A d L}right] )
c. ( _{sigma}=frac{1}{2} frac{d V}{A d L} )
D. ( sigma=frac{d V}{A d L} )
11
794A metal wire of length L is loaded and an
elongation of ( Delta L ) is produced. If the area of cross section of the wire is ( A ) then the change in volume of the wire, when elongated is. Take Poisson’s ratio
as 0.25
A ( cdot Delta V=(Delta L)^{2} A / L )
B . ( Delta V=(Delta L)^{2} A / 4 L )
c. ( Delta V=(Delta L)^{2} A / 2 L )
D. ( Delta V=(Delta L)^{2} A / 3 L )
11
795The ratio of modulus of rigidity to bulk modulus for a Poisson’s ratio of 0.25
would be
A. ( 2 / 3 )
в. ( 2 / 5 )
( c .3 / 5 )
D. 1.0
11
796Two wires are made of the same
material and have the same volume.
The first wire has cross-sectional area ( A ) and the second wire has cross-sectional
area 3 A. If the length of the first wire is
increased by ( Delta l ) on applying a force ( F ) how much force is needed to stretch the
second wire by the same amount?
A . 4 F
B. 9 F
( c . F )
D. 6 F
11
797Choose the correct statements from the
following:
This question has multiple correct options
A. Steel is more elastic than rubber.
B. The stretching of a coil spring is determined by the young’s modulus of the wire of the spring.
C. The frequency of a tuning fork is determined by the shear modulus of the material of the fork.
D. When a material is subjected to a tensile (stretching) stress the restoring forces are caused by interatomic attraction.
11
798A wire of lenth L suppleid heat to raise its temperature by T.if y is the coefficient of volume expansion of the wire and Young’s modulus of the wire
then the energy density stored in the wire is.
11
799A wire elongates by ( l ) mm when a load
( W ) is hanged from it. If the wire goes over a pulley and two weights ( W ) each are hung at the two ends, the elongation of the wire will be (in ( m m ) ):
A . 1
в. 2
c. zero
D. ( l / 2 )
11
800A metal cube of side ( 10 mathrm{cm} ) is subjected
to a shearing stress of ( 10^{4} N m^{-2} ). The modulus of rigidity if the top of the cube is displaced by ( 0.05 mathrm{cm} ) with respect to its bottom is
A . ( 2 times 10^{6} mathrm{Nm}^{-2} )
B. ( 10^{5} N m^{-2} )
c. ( 1 times 10^{7} N m^{-2} )
D. ( 4 times 10^{5} mathrm{Nm}^{-2} )
11
801In steel, the Young’s modulus and the strain at the breaking point are ( 2 times ) ( 10^{11} N / m^{2} ) and 0.15 respectively. The
stress at the breaking point for steel is therefore:
A ( cdot 1.33 times 10^{11} mathrm{Nm}^{-2} )
В. ( 1.33 times 10^{12} mathrm{Nm}^{-2} )
c. ( 7.5 times 10^{-13} mathrm{Nm}^{-2} )
D. ( 3 times 10^{10} mathrm{Nm}^{-2} )
11
802The relationship between ( Y, eta ) and ( sigma ) is
( mathbf{A} cdot Y=2 eta(1+sigma) )
B ( . eta=2 Y(1+sigma) )
c. ( sigma=frac{2 Y}{(1+eta)} )
D. ( Y=eta(1+sigma) )
11
803Possible value of Poisson’s ratio is
( A )
B. 0.9
( c cdot 0.8 )
D. 0.4
11
804A wire of length L and radius r fixed at
one end and a force ( F ) applied to the other end produces and extension ( l ). The
extension produced in another wire of the same material of length 2Land radius ( 2 r ) by a force ( 2 F ) is:
( mathbf{A} cdot l )
в. ( 2 l )
( c cdot frac{l}{2} )
D. 4
11
805A weight is suspended from a long metal wire. If the wire suddenly breaks, its temperature.:-
A . rises
B. falls
c. remains unchanged
D. attains a velue ( 0 K )
11
806Steel wire of length ‘ ( L ) ‘ at ( 40^{circ} mathrm{C} ) is suspended from the ceiling and then a mass ‘ ( m^{prime} ) is hung from its free end. The
wire is cooled down from ( 40^{circ} C ) to ( 30^{circ} C )
to regain its original length ( ^{prime} L^{prime} . ) The coefficient of linear thermal expansion
of the steel is ( 10^{-5} /^{circ} C, ) Young’s modulus of steel is ( 10^{11} N / m^{2} ) and radius of the wire is ( 1 mathrm{mm} ). Assume that
( L>> ) diameter of the wire. Then the
value of ‘ ( m ) ‘ in kg is nearly
A . 3
B. 2
( c .9 )
D. 5
11
807A wire of length L and Density ( phi ) and young’s modulus Y is hanging from a support .Find the elongation in the length of the wire at which wire will break:
( mathbf{A} cdot frac{L^{2} phi g}{Y} )
B. ( frac{L^{2} phi g}{2 Y} )
( ^{mathrm{c}} cdot frac{2 L^{2} phi g}{Y} )
D. ( frac{L^{2} phi g}{4 Y} )
11

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