For a monoatomic gas, the work done at constant pressure is '$$\mathrm{W}$$' The heat supplied at constant volume for the same rise in temperature of the gas is

$$[\gamma=\frac{C_p}{C_v}=\frac{5}{2}$$ for monoatomic gas]

A thin metal disc of radius 'r' floats on water surface and bends the surface downwards along the perimeter making an angle '$$\theta$$' with the vertical edge of the dsic. If the weight of water displaced by the disc is '$$\mathrm{W}$$', the weight of the metal disc is [T = surface tension of water]

A particle performing linear S.H.M. of amplitude $$0.1 \mathrm{~m}$$ has displacement $$0.02 \mathrm{~m}$$ and acceleration $$0.5 \mathrm{~m} / \mathrm{s}^2$$. The maximum velocity of the particle in $$\mathrm{m} / \mathrm{s}$$ is

The electric field intensity on the surface of a charged solid sphere of radius '$$r$$' and volume charge dentiy '$$\rho$$' is given by ($$\epsilon_0=$$ permittivity of free space)