A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 $$ \times $$ 10^–2 N/m. The pressure inside the bubble equals at a point Z₀ below the free surface of water in a container. Taking g = 10 m/s², density of water = 10³ kg/m³, the value of Z₀ is :

The power radiated by a black body is P and it radiates maximum energy at wavelength, $$\lambda $$₀ . If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $${3 \over 4}{\lambda _0}$$, the power radiated by it becomes nP. The value of n is

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by $$\Delta $$l on applying a force F, how much force is needed to stretch the second wire by the same amount?

A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to