Practice Test

1) Two bars A and B of circular cross-section and of same volume and made of the same material are subjected to tension. If the diameter of A is half that of B and if the force applied to both the rods is the same and it is in the elastic limit, the ratio of extension of A to that of B will be

2) Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows

3) The bulk modulus of an ideal gas at constant temperature

4) Two wires of same material and radius have their lengths in ratio 1:2. If these wires are stretched by the same force, the strain produced in the two wires will be in the ratio

5) If a bar is made of copper whose coefficient of linear expansion is one and a half times that of iron, the ratio of the force developed in the copper bar to the iron bar of identical lengths and cross-sections, when heated through the same temperature range (Young’s modulus for copper may be taken equal to that of iron) is

6) To break a wire of one metre length, minimum 40 kg wt, is required. Then the wire of the same material of double radius and 6 m length will require breaking weight

7) The Young’s modulus of the material of a wire is equal to the

8) When a certain weight is suspended from a long uniform wire, its length increases by 1 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

9) A force F is required to break a wire of length l and radius r. What force is required to break a wire, of the same material, having twice the length and six times the radius ?

10) To keep constant time, watches are fitted with balance wheel made of

11) Young’s modulus of perfectly rigid body material is

12) A wire can be broken by applying a load of 200 N. The force required to break another wire of the same length and same material, but double in diameter, is

13) When a weight of 10 kg is suspended from a copper wire of length 3 metres and diameter 0.4 mm, its length increases by 2.4 cm. If the diameter of the wire is doubled, then the extension in its length will be

14) The 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?

15) The mass and length of a wire are M and L respectively. The density of the material of the wire is d. On applying the force F on the wire, the increase in length is l, then the Young’s modulus of the material of the wire will be

16) Wires A and B are made from the same material. A has twice the diameter and three times the length of B.
If the elastic limits are not reached, when each is stretched by the same tension, the ratio of energy stored
in A to that in B is

17) Calculate the work done, if a wire is loaded by ′Mg′ weight and the increase in length is ′l′

18) A metallic ring of radius r and cross-sectional area A is fitted into a wooden circular disc 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

19) A cube is shifted to a depth of 100 m in a lake. The change in volume is 0.1%. The bulk modulus of the
material is nearly

20) Forces of 100 N each are applied in opposite directions on the upper and lower faces of a cube of side 20
cm. The upper face is shifted parallel to itself by 0.25 cm. If the side of the cube were 10 cm, then the
displacement would be

21) Which of the following statements is correct

22) Two identical wires are suspended from the same rigid support but one is of copper and the 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

23) A 100 N force stretches the length of a hanging wire by 0.5 mm. The force required to stretch a wire, of the same material and length but having four times the diameter, by 0.5 mm is

24) If a spring extends by x on loading, then the energy stored by the spring is (if T is tension in the spring and k is spring constant)

25) A wire is stretched 1 mm by a force of 1 k N. How far would a wire of the same material and length but of four times that diameter be stretched by the same force ?

26) A wire of natural length l, Young’s modulus Y and area of cross-section A is extended by x. Then the energy stored in the wire is given by

27) Young’s modulus of the wire depends on

28) An elastic material of Young’s modulus Y is subjected to a stress S. The elastic energy stored per unit volume of the material is

29) A wire fixed at the upper end stretches by length by applying a force F. The work done in stretching is

30) If work done in stretching a wire by 1 mm is 2 J, the work necessary for stretching another wire of same material, but wire double the radius and half length 1 mm joule is

31) A load W produces an extension of 1mm in a thread of radius r. Now if the load is made 4W and radius is made 2r all other things remaining same, the extension will become

32) A cube is subjected to a uniform volume compression. It the side of the cube decreases by 2%, the bulk strain is

33) X linear strain is produced in a wire of elasticity coefficient Y. The stored potential energy in unit volume of this wire is

34) A wire of length L and cross-section A is made of material of Young’s modulus Y. It is stretched by an amount x, the work done is

35) A body of mass m is suspended to an ideal spring of force constant k. The expected change in the position of the body due to an additional force F acting vertically downwards is

36) A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is

37) Two wires of the same material and length but diameters in the ratio 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

38) The increase in pressure required to decrease the 200 L volume of a liquid by 0.008% in kPa is (Bulk modulus of the liquid = 2100 MPa is)

39) A wire is stretched by 0.01 m by a certain force F. Another wire of same material whose diameter and length are double to the original wire is stretched by the same force. Then its elongation will be

40) A 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 mm)

41) A wire of length L and radius a rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2a is stretched with a force 2F, the increase in its length will be

42) A force F is needed to break a copper wire having radius R. The force needed to break a copper wire of radius 2R will be

43) A load suspended by a massless spring produces an extension of x cm in equilibrium. When it is cut into two unequal parts, the same load produces an extension of 7.5 cm when suspended by the larger part of length 60 cm. When it is suspended by the smaller part, the extension is 5.0 cm. Then

44) A pan with set of weights is attached with a light spring. When disturbed, the mass-spring system oscillates with a time period of 0.6 s. When some additional weights are added then time period is 0.7 s. The extension caused by the additional weights is approximately given by

45) If x longitudinal strain is produced in a wire of Young’s modulus y, then energy stored in the material of the wire per unit volume is

46) The Poisson’s ratio of a material is 0.4. If a force is applied to a wire of this material, there is decrease of
cross-sectional area by 2%. The percentage increase in its length is

47) The possible value of Poisson’s ratio is

48) A steel wire is stretched with a definite load. If the Young’s modulus of the wire is Y. For decreasing the
value of Y

49) A uniform wire, fixed at its upper end, hangs vertically and supports a weight at its lower end. If its radius
is r, its length L and the Young’s modulus for the material of the wire is E, the extension is
1. directly proportional to E
2. inversely proportional to r
3. directly proportional to L

50) For most materials the Young’s modulus is n times the rigidity modulus, where n is

51) When a weight of 5 kg is suspended from a copper wire of length 30 m and diameter 0.5 mm, the length of
the wire increases by 2.4 cm. If the diameter is doubled, the extension produced is

52) A fixed volume of iron is drawn into a wire of length L. The extension x produced in this wire by a constant force F is proportional to

53) The lower surface of a cube is fixed. On its upper surface, force is applied at an angle of 30° from its surface. The change will be of the type

54) A copper wire and a steel wire of the same diameter and length are connected end to end and a force is applied, which stretches their combined length by 1 cm. The two wires will have

55) Which of the following substance has the highest elasticity?

56) If the force constant of a wire is K, the work done in increasing the length of the wire by l is

57) The elastic energy stored in a wire of Young’s modulus Y is

58) Two wires of equal lengths are made of the same material. Wire A has a diameter that is twice as that of wire B. If identical weights are suspended from the ends of these wires, the increase in length is

59) A metallic rod of length l and cross-sectional area A is made of a material of Young modulus Y. If the rod is elongated by an amount y, then the work done is proportional to

60) A wire fixed at the upper end stretches by length l by applying a force F. The work done in stretching is

61) The isothermal elasticity of a gas is equal to

62) If S is stress and Y is Young’s modulus of material of a wire, the energy stored in the wire per unit volume
is

63) A cube of aluminium of sides 0.1 m is subjected to a sharing force of 100 N. The top face of the cube is
displaced through 0.02 cm with respect to the bottom face. The shearing strain would be

64) Which of the following rods of same material undergoes maximum elongation when subjected to a given
force?

65) A wire suspended vertically from one of its ends is 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

66) If in a wire of Young’s modulus Y, longitudinal strain X is produced then the potential energy stored in its
unit volume will be

67) Two wires of the same length and same material but radii in the ratio of 1 : 2 are stretched by unequal
forces to produce equal elongation. The ratio of the two forces is

68) The force constant of a wire is k and that of another wire of the same material is 2k. When both the wires are stretched, then work done is

69) A wire is stretched under a force. If the wire suddenly snaps the temperature of the wire

70) A 2 m long rod of radius 1 cm which is fixed from one end is given a twist of 0.8 radians. The shear strain developed will be

71) The length of a wire is increased by 1 mm 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 the application of the same load, extension is

72) The upper end of a wire 1 m long and 2 mm radius is clamped. The lower end is twisted through and angle of 45°. The angle of shear is

73) The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum ?

74) Which statement is true for a metal

75) Two wires of copper having the length in the ratio 4:1 and their radii ratio as 1:4 are stretched by the same force. The ratio of longitudinal strain in the two will be

76) Two wires A and B of same length, same area of cross-section having the same Young’s modulus are heated to the same range of temperature. If the coefficient of linear expansion of A is 3/2 times of that of wire B. The ratio of the forces produced in two wires will be

77) A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to

78) Which one of the following statements is correct? In the case of

79) If the Young’s modulus of the material is 3 times its modulus of rigidity, then its volume elasticity will be

80) When 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

81) On stretching a wire, the elastic energy stored per unit volume is

82) The work done in deforming body is given by

83) The Bulk modulus for an incompressible liquid is

84) Two wires of lengthl, radius r and length 2l, radius 2r respectively having some Young’s modulus are hung with a weight mg. Net elongation is

85) A wire of length L and radius r fixed at one end and a force F applied to the other end produces an extensionl. The extension produced in another wire of the same material of length 2L and radius 2r by a force 2F, is

86) The breaking stress of a wire depends upon

87) Young’s modulus of the material of a wire is Y. On pulling the wire by a force F, the increase in its length is x. The potential energy of the stretched wire is

88) Energy stored in stretching a string per unit volume is

89) What is the increase in elastic potential energy when the stretching force is increased by 200 kN?

90) The radii and Young’s modulii of two uniform wiresA 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

91) The increase in length on stretching a wire is 0.05%. If its Poisson’s ratio is 0.4, the diameter is reduced by

92) Which of the following substances has the highest elasticity?

93) For a given material, the Young’s modulus is 2.4 times that of rigidity modulus. Its Poisson’s ratio is

94) A spring of constant k is cut into parts of length in the ratio 1 : 2. The spring constant of larger on is 0

95) A uniform plank of Young’s modulus Y is moved over a smooth horizontal surface by a constant force F. The area of cross section of the plank is A. The compressive strain on the plank in the direction of the force is

96) A wire of length L and area of cross-section A is stretched through a certain length l. If Y is Young’s modulus of the material of the wire, then the force constant of the wire is

97) For a given material, the Young’s modulus is 2.4 times that of modulus of rigidity. Its Poisson’s ratio is

98) The value of Poisson’s ratio lies between

99) The increases in length is l of a wire of length L by the longitudinal stress. Then the stress is proportional to

100) A wire of diameter 1mm breaks under a tension of 1000 N. Another wire, of same material as that of the first one, but of diameter 2 mm breaks under a tension of

101) A rope 1cm in diameter breaks, if the tension in it exceeds 500 N. The maximum tension that may be given to similar rope of diameter 3 cm is

102)
A rod elongated by l when a body of mass M is suspended from it. The work done is

103) The only elastic modulus that applies to fluids is

104) A gas has Bulk modulus K and natural density ρ. If pressure p is applied, what is change in density?

105) The Poisson’s ratio cannot have the value

106) Two identical wires of rubber and iron are stretched by the same weight, then the number of atoms in the iron wire will be

107) The ratio of the adiabatic to isothermal elasticities of a triatomic gas is

108) If the work done in stretching a wire by 1 mm 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

109) A wire is loaded by 6 kg at its one end, the increase in length is 12 mm. If the radius of the wire is doubled and all other magnitudes are unchanged, then increase in length will be

110) After effects of elasticity are maximum for

111) Modulus of rigidity of a liquid

112) If the length of a wire is reduced to half, then it can hold the ………. load

113) Which of the following relation is true?

114) There are two wires of the same length. The diameter of second wire is twice that of the first. On applying the same load to both the wires, the extension produced in them will be in ratio of

115) The extension in a string obeying Hooke’s law is x. The speed of sound in the stretched string is v. If the extension in the string is increased to 1.5 x, the speed of sound will be

116) What among of work is done in increasing the length of a wire though unity ?

117) Write copper, steel, glass and rubber in order of increasing coefficient of elasticity.

118) Two wires of same diameter of the same material having the length l and 2l. If the force F is applied on each, the ratio of the work done in the two wires will be

119) There is no change in the volume of a wire due to the change in its length on stretching. The Poisson’s ratio of the material of the wire is

120) A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1mm. Then, the elastic energy stored in the wire is

121) The ratio of diameters of two wires of same materials is n: 1. The length of each wire is 4 m. On applying the same load, the increase in length of thin wire will be (n>1)

122) Shearing stress causes change in

123) A cube is subjected to a uniform volume compression. If the side of the cube decreases by 1% the bulk strain is

124) In the three states of matter, the elastic coefficient can be

125) Two pieces of wire A and B of the same material have their lengths in the ratio 1 : 2, and their diameters are in the ratio 2 : 1. If they are stretched by the same force, their elongations will be in the ratio

126) A 5 metre long wire is fixed to the ceiling. A weight of 10 kg 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 stretching is

127) Which one of the following quantities does not have the unit of force per unit area

128) A wire extends by 1 mm when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross-section. The elongation of the wire in mm will be

129) According to Hooke’s law of elasticity, if stress is increased, them the ratio of stress to strain

130) The twisting couple per unit twist for a solid cylinder of radius 3 cm is 0.1 N-m. The twisting couple per unit twist, for a hollow cylinder of same material with outer and inner radius 5 cm and 4 cm respectively will be

131) Which of the following relations is true

132) Two 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

133) Stress to strain ratio is equivalent to

134) The material which practically does not show elastic after effect is

135) If the thickness of the wire is doubled, then the breaking force in the above question will be

136) If a spring is extended to length l, then according to Hooke’s law

137) Mark the wrong statement

138) When a 4 kg mass is hung vertically on a light spring that obeys Hook’s law, the spring stretches by 2 cm. The work required to be done by an external agent in stretching this spring by 5 cm will be

139) There 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 wire is

140) A height spring extends 40 mm when stretched by a force of 10 N, and for tensions up to this value the extension is proportional to the stretching force. Two such springs are joined end-to-end and the double- length spring is stretched 40 mm beyond its natural length. The total strain energy in (joule), stored in the double spring is

141) The upper end of a wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through and angle of 30°. Then angle of shear is

142) The isothermal bulk modulus of a gas at atmospheric pressure is

143) There are two wires of same material and same length while the diameter of second wire is 2 times the diameter of first wire, then ratio of extension produced in the wires by applying same load will be

144) A copper rod of length L and radius ris suspended from the ceiling by one of its ends. What will be elongation of the rod due to its own weight when ρand Y are the density and Young’s modulus of the copper respectively?

145) An iron bar of length L, cross-section A and Young’s modulus Y is pulled by a force F from both ends so as to produce an elongation l. Which of the following statement is correct?

146) When a weight w is hung from one and of the wire other end being fixed, the elongation produced in it be l. If this wire goes over a pulley and two weights w each are hung at the two ends, the elongation of the wire will be

147) A spring is extended by 30 mm when a force of 1.5 N is applied to it. Calculate the energy stored in the spring when hanging vertically supporting a mass of 0.20 kg if the spring was instructed before applying the mass.

148) 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

149) If longitudinal strain for a wire is 0.03 and its Poisson’s ratio is 0.5, then its lateral strain is

150) Under elastic limit the stress is

151) A cube of side 40 mm has its upper face displaced by 0.1 mm by a tangential force of 8 kN. The shearing modulus of cube is

152) Which is the most elastic

153) A solid sphere of radius R made up of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area 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

154) A steel ring of radius r and cross-section area 'A' is fitted on to a wooden disc of radius R(R>r). If Young’s modulus be E, then the force with which the steel ring is expanded is

155) If the compressibility of water is σ per unit atmospheric pressure, then the decrease in volume (V) due to atmospheric pressure p will be

156) Identify the incorrect statement