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

If in case A, elongation in wire of length L is l, then for same wire, elongation in case B will be-

1. 4l

2. 2l

3. l

4. l/2