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]

The surface energy of a liquid drop is 'U'. It splits up into 512 equal droplets. The surface energy becomes

Air is pushed in a soap bubble to increase its radius from 'R' to '2R'. In this case, the pressure inside the bubble

Let '$$\mathrm{R_1}$$' and '$$\mathrm{R_2}$$' are radii of two mercury drops. A big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is