When a rubber ball is taken to the bottom of a sea of depth 1400 m, its volume decreases by 2%. The Bulk Modulus of rubber ball is [density of water is 1 g cc and $\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2$]

1. $7\times {10}^8 \mathrm{N}/{\mathrm{m}}^2$

2. $2\times {10}^8 \mathrm{N}/{\mathrm{m}}^2$

3. $2.5\times {10}^8 \mathrm{N}/{\mathrm{m}}^2$

4. $9\times {10}^8 \mathrm{N}/{\mathrm{m}}^2$

A spherical ball contracts in volume by 0.02%, when subjected to a normal uniform pressure of 50 atmosphere. The Bulk Modulus of its material is

1. $1\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2$

2. $2\times {10}^{10} \mathrm{N}/{\mathrm{m}}^2$

3. $2.5\times {10}^{10} \mathrm{N}/{\mathrm{m}}^2$

4. $1\times {10}^{13} \mathrm{N}/{\mathrm{m}}^2$

For an elastic material

1. $\mathrm{\gamma }>\mathrm{\eta }$

2. $\mathrm{\gamma }<\mathrm{\eta }$

3. $\mathrm{\gamma \eta }=1$

4. $\mathrm{\gamma }=\mathrm{\eta }$

Correct pair is

1. Change in shape - Longitudinal strain

2. Change in volume - Shear strain

3. Change in length - Bulk strain

4. Reciprocal of Bulk Modulus - Compressibility

The breaking stress of aluminium is $7.5\times {10}^7 {\mathrm{Nm}}^{-2}$. The greatest length of aluminium wire that can hang vertically without breaking is
(Density of aluminium is $2.7\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$)

1. $283\times {10}^3 \mathrm{m}$

2. $28.3\times {10}^3 \mathrm{m}$

3. $2.83\times {10}^3 \mathrm{m}$

4. $0.283\times {10}^3 \mathrm{m}$

A wire is 2 m in length suspended vertically stretches by 10 mm when mass of 10 kg is attached to the lower end. The elastic potential energy gain by the wire is (take $\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2$)

1. 0.5 J

2. 5 J

3. 50 J

4. 500 J

A wire of length L and cross-sectional area A is made of material of Young's Modulus Y. The work done in stretching the wire by an amount x is

1. $\frac{{\mathrm{YAx}}^2}{\mathrm{L}}$

2. $\frac{{\mathrm{YAx}}^2}{2\mathrm{L}}$

3. $\frac{2{\mathrm{YAx}}^2}{\mathrm{L}}$

4. $\frac{4{\mathrm{YAx}}^2}{\mathrm{L}}$

Two exactly similar wires of steel and copper are stretched by equal forces. If the total elongation is 2 cm, then how much is the elongation in steel and copper wire respectively? Given, ${\mathrm{Y}}_{\mathrm{steel}}=20\times {10}^{11} \mathrm{dyne}/{\mathrm{cm}}^2, {\mathrm{Y}}_{\mathrm{copper}}=12\times {10}^{11} \mathrm{dyne}/{\mathrm{cm}}^2.$

1. 1.25 cm; 0.75 cm

2. 0.75 cm; 1.25 cm

3. 1.15 cm; 0.85 cm

4. 0.85 cm; 1.15 cm

The proportional limit of steel is $8\times {10}^8 \mathrm{N}/{\mathrm{m}}^2$ and its Young's Modulus is $2\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2$. The maximum elongation, a one metre long steel wire can be given without exceeding the proportional limit is

1. 2 mm

2. 4 mm

3. 1 mm

4. 8 mm

In a series combination of copper and steel wires of same length and same diameter, a force is applied at one of their ends while the other end is kept fixed. The combined length is increased by 2 cm. The wires will have

1. Same stress and same strain

2. Different stress and different strain

3. Different stress and same strain

4. Same stress and different strain