A small ball of mass $$\mathrm{M}$$ and density $$\rho$$ is dropped in a viscous liquid of density $$\rho_{0}$$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?

The Young's modulus of a steel wire of length $$6 \mathrm{~m}$$ and cross-sectional area $$3 \mathrm{~mm}^{2}$$, is $$2 \times 10^{11}~\mathrm{N} / \mathrm{m}^{2}$$. The wire is suspended from its support on a given planet. A block of mass $$4 \mathrm{~kg}$$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $$\frac{1}{4}$$ of its value on the earth. The elongation of wire is (Take $$g$$ on the earth $$=10 \mathrm{~m} / \mathrm{s}^{2}$$) :

The average kinetic energy of a molecule of the gas is

A mercury drop of radius $$10^{-3}~\mathrm{m}$$ is broken into 125 equal size droplets. Surface tension of mercury is $$0.45~\mathrm{Nm}^{-1}$$. The gain in surface energy is :