Mechanical Properties of Solids

The density and breaking stress of a wire are 6 104 kg/m3 and 1.2 108 N/m2 respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is 13rd of the value on the surface of earth. The maximum length of the wire without breaking is m (take, g = 10 m/s2).

Match List I with List II : Choose the correct answer from the options given below :

1. (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
2. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
3. (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
4. (A)-(III), (B)-(I), (C)-(II), (D)-(IV)

An elastic spring under tension of 3 N has a length a. Its length is b under tension 2 N. For its length (3a-2b), the value of tension will be N.

With rise in temperature, the Young's modulus of elasticity :

1. changes erratically
2. increases
3. decreases
4. remains unchanged

One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be . [Area of cross section of wire =0.005 cm2, Y=2 1011 Nm-2 and g=10 ms-2]

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0.02\% is m. (Take density of sea water =103 kgm-3, Bulk modulus of rubber =9 108 Nm-2, and g=10 ms-2)

Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is 4.0 10-5 m and Young's modulus of the metal is 2.0 1011 N/m2. The longitudinal strain developed in the wire is 1 . The value of is . [Use g=10 m/s2] [figure]

Young's modulus of material of a wire of length 'L' and cross-sectional area A is Y. If the length of the wire is doubled and cross-sectional area is halved then Young's modulus will be :

1. 4 Y
2. 2 Y
3. Y4
4. Y

Each of three blocks P, Q and R shown in figure has a mass of 3 kg. Each of the wires A and B has cross-sectional area 0.005 cm2 and Young's modulus 2 1011 N m-2. Neglecting friction, the longitudinal strain on wire B is 10-4. (Take g=10 m/s2) [figure]

A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F, its length increases by l. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

1. 2 times
2. 4 times
3. 3 times
4. 32 times