A liquid drop of radius '$$R$$' is broken into '$$n$$' identical small droplets. The work done is [T = surface tension of the liquid]

For a gas, $$\frac{\mathrm{R}}{\mathrm{C}_{\mathrm{v}}}=0 \cdot 4$$, where $$\mathrm{R}$$ is universal gas constant and $$\mathrm{C}_{\mathrm{v}}$$ is molar specific heat at constant volume. The gas is made up of molecules which are

Two bodies $$\mathrm{A}$$ and $$\mathrm{B}$$ at temperatures '$$\mathrm{T}_1$$' $$\mathrm{K}$$ and '$$\mathrm{T}_2$$' $$\mathrm{K}$$ respectively have the same dimensions. Their emissivities are in the ratio $$1: 3$$. If they radiate the same amount of heat per unit area per unit time, then the ratio of their temperatures $$\left(\mathrm{T}_1: \mathrm{T}_2\right)$$ is

In a conical pendulum the bob of mass '$$\mathrm{m}$$' moves in a horizontal circle of radius '$$r$$' with uniform speed '$$\mathrm{V}$$'. The string of length '$$\mathrm{L}$$' describes a cone of semi vertical angle '$$\theta$$'. The centripetal force acting on the bob is ( $$\mathrm{g}=$$ acceleration due to gravity)