Mechanical Properties of Solids · Question 4

Two wires as shown in the figure below, made of steel and have breaking stress of 12 108 N/m2. Area of cross-section of upper wire is 0.008 cm2 and of lower wire is 0.004 cm2. The maximum mass that can be added to pan without breaking any wire is kg. [figure]

1. 56
2. 38
3. 96
4. 5.6

A cube has side length 5 cm and modulus of rigidity 105 N/m2. The displacement produced by a force of 10 N in the upper face of cube is mm.

A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is 600 10-6 m3. The elastic potential energy stored in the wire in stretched condition would be J. (Given Young modulus of copper = 1.1 1011 N/m2)

The increase in the pressure required to decrease the volume ( V) of water is 6.3 107 N/m2. The percentage decrease in the volume is . (Bulk modulus of water =2.1 109 N/m2.)

1. 2 %
2. 3 %
3. 6 %
4. 4 %

A string A of length 0.314 m and Young's modulus 2 1010 N/m2 is connected to another string B of length and Young's modulus both twice of those of A. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg. The net change in length of the combination is mm. (radius of both the strings is 0.2 mm and acceleration due to gravity = 10 m/s2) (Mass of both strings is to be neglected as compared to the mass of load)

1. 3
2. 2
3. 1.9
4. 1

A metal string A is suspended from a rigid support and its free end is attached to a block of mass M. Second block having mass 2M is suspended at the bottom of the first block using a string B. The area of cross sections of strings A and B are same. The ratio of lengths of strings of A to B is 2 and the ratio of their Young's moduli (YA/YB ) is 0.5. The ratio of elongations in A to B is .

1. 1
2. 4
3. 8
4. 6

A uniform wire of length l of weight w is suspended from the roof with a weight of W at the other end. The stress in the wire at l3 distance from the top is ( WA+ 2 wA ), where A is the cross sectional area of the wire. The value of is .

Two wires A and B made of different materials of lengths 6.0 cm and 5.4 cm, respectively and area of cross sections 3.0 10-5 m2 and 4.5 10-5 m2, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of A to that of B is x : 3. The value of x is

1. 2
2. 1
3. 4
4. 5

The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus ? [figure]

1. B
2. A
3. D
4. C

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is P 1011 N m-2, where the value of P is: (Take g = 3 m/s2)

1. 2.5
2. 25
3. 10
4. 5