The velocity of a small ball of mass '$$M$$' and density '$$\mathrm{d}_1$$' when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is '$$\mathrm{d}_2$$', the viscous force acting on the ball is ( $$\mathrm{g}=$$ acceleration due to gravity)

Two small drops of mercury each of radius '$$R$$' coalesce to form a large single drop. The ratio of the total surface energies before and after the change is

What should be the radius of water drop so that excess pressure inside it is 72 Nm$$^{-2}$$ ? (The surface tension of water 7.2 $$\times$$ 10$$^{-2}$$ Nm$$^{-1}$$)

A body of density $$V$$ is dropped from (at rest) height '$$h$$' into a lake of density '$$\delta$$' $$(\delta > \rho)$$. The maximum depth to which the body sinks before returning to float on the surface is [Neglect all dissipative forces]