A certain gas is isothermally compressed to $\left(\frac{1}{3}\right)^{\mathrm{rd}}$ of its initial volume $\left(V_{\mathrm{o}}=3\right.$ litre) by applying required pressure. If the bulk modulus of the gas is $3 \times 10^5 \mathrm{~N} / \mathrm{m}^2$, the magnitude of work done on the gas is $\_\_\_\_$ J.

A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is $600 \times 10^{-6} \mathrm{~m}^3$. The elastic potential energy stored in the wire in stretched condition would be

$\_\_\_\_$ J.

(Given Young modulus of copper $=1.1 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$ )

A cube has side length 5 cm and modulus of rigidity $10^5 \mathrm{~N} / \mathrm{m}^2$. The displacement produced by a force of 10 N in the upper face of cube is $\_\_\_\_$ mm.

The surface tension of a soap solution is $3.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is $\alpha \times 10^{-6} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$ .

$$ (\pi=22 / 7) $$