Mechanical Properties of Solids

The fractional compression ( VV ) of water at the depth of 2.5 km below the sea level is %. Given, the Bulk modulus of water = 2 109 N m-2, density of water = 103 kg m-3, acceleration due to gravity g = 10 m s-2.

1. 1.0
2. 1.25
3. 1.75
4. 1.5

The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of 7 106 Pa, would be mm3. (Given bulk modulus of copper = 1.4 1011 N m-2)

The increase in pressure required to decrease the volume of a water sample by 0.2\% is P 105 Nm-2. Bulk modulus of water is 2.15 109 Nm-2. The value of P is .

A massless spring gets elongated by amount x1 under a tension of 5 N. Its elongation is x2 under the tension of 7 N. For the elongation of (5x1-2x2), the tension in the spring will be,

1. 20 N
2. 39 N
3. 11 N
4. 15 N

Two persons pull a wire towards themselves. Each person exerts a force of 200 N on the wire. Young's modulus of the material of wire is 1 1011 N m-2. Original length of the wire is 2 m and the area of cross section is 2 cm2. The wire will extend in length by .

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