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

Energy stored per unit volume in a stretched wire having Young's Modulus Y and stress 'S' is

1. $\frac{\mathrm{YS}}{2}$

2. $\frac{{\mathrm{S}}^2\mathrm{Y}}{2}$

3. $\frac{{\mathrm{S}}^2}{2\mathrm{Y}}$

4. $\frac{\mathrm{S}}{2\mathrm{Y}}$

A wire suspended vertically from one end and is stretched by attaching a weight 200 N to the lower end. The weight stretches the wire by 1 mm. The elastic potential energy gained by the wire is

1. 0.1 J

2. 0.2 J

3. 0.4 J

4. 10 J

Work done by restoring force in a wire within elastic limit is -10 J. Maximum amount of heat produced in the wire is

1. 10 J

2. 20 J

3. 5 J

4. 15 J

The work done per unit volume to stretch the length of area of cross-section 2 mm² by 2% will be
$\left[\mathrm{Y}=8\times {10}^{10} \mathrm{N}/{\mathrm{m}}^2\right]$

1. 40 MJ/m³ 

2. 16 MJ/m³ 

3. 64 MJ/m³ 

4. 32 MJ/m³