A steel rod with y = 2.0 $$\times$$ 10¹¹ Nm^$$-$$2 and $$\alpha$$ = 10^$$-$$5 $$^\circ$$C^$$-$$1 of length 4 m and area of cross-section 10 cm² is heated from 0$$^\circ$$C to 400$$^\circ$$C without being allowed to extend. The tension produced in the rod is x $$\times$$ 10⁵ N where the value of x is ____________.

When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases by 0.5%.

(The bulk modulus of rubber = 9.8 $$\times$$ 10⁸ Nm^$$-$$2, Density of sea water = 10³ kgm^$$-$$3, g = 9.8 m/s²)

Wires W₁ and W₂ are made of same material having the breaking stress of 1.25 $$\times$$ 10⁹ N/m². W₁ and W₂ have cross-sectional area of 8 $$\times$$ 10^$$-$$7 m² and 4 $$\times$$ 10^$$-$$7 m², respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is ____________ kg. (Use g = 10 m/s²)

A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ................ cm.