Mechanical Properties of Solids

A wire of cross sectional area A, modulus of elasticity 2 1011 Nm-2 and length 2 m is stretched between two vertical rigid supports. When a mass of 2 kg is suspended at the middle it sags lower from its original position making angle = 1100 radian on the points of support. The value of A is 10-4 m2 (consider x L). (given : g = 10 m/s2) [figure]

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]