A polyatomic gas is compressed to $\left(\frac{1}{8}\right)^{\text {th }}$ of its volume adiabatically. If its initial pressure is $\mathrm{P}_0$, its new pressure will be [Given, $\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{4}{3}$ ]

A particle is executing linear S.H.M. starting from mean position. The ratio of the kinetic energy to the potential energy of the particle at a point of half the amplitude is

A parallel plate air capacitor has capacity ' $C$ ' and distance of separation between plates is ' $d$ '. If a conducting sheet of thickness $\frac{2 d}{3}$ is inserted in between the plates, the capacitance becomes $C_1$. The ratio of $\frac{C_1}{C}$ is

A uniform solid sphere of mass ' $m$ ' and radius ' r ' is surrounded by a uniform thin spherical shell of radius ' $2 r$ ' and mass ' $m$ ' then the gravitational field