Mechanical Properties of Solids

The two wires A and B of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire A and wire B is 20/11. When the joined wire is kept under certain tension the elongations in the wires A and B are equal. If the length of wire A is 2.2 m, then the length of wire B is m.

1. 1.1
2. 2.22
3. 1.21
4. 4.44

Figure represents the extension ( l) of a wire of length 1 meter, suspended from the ceiling of the room at one end with a load W connected to the other end. If the cross-sectional area of the wire is 10-5 m2 then the Young's modulus of the wire is N/m2. [figure]

1. 1.0 1011
2. 2.0 1010
3. 1.0 1010
4. 2.0 1011

The Young's modulus of steel wire of radius r and length L is Y. If the radius r and length L of the wire are doubled then the value of Y

1. increases by two times
2. reduces by half
3. remains unchanged
4. becomes one fourth

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

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

Two wires A and B are made of same material having ratio of lengths LALB = 13 and their diameters ratio dAdB = 2. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

1. 3 : 4
2. 1 : 12
3. 1 : 3
4. 1 : 6