A diatomic gas $\left(\gamma=\frac{7}{5}\right)$ is compressed adiabatically to volume $\frac{\mathrm{V}_0}{32}$, where $\mathrm{V}_0$ is its initial volume. The initial temperature of the gas is $\mathrm{T}_{\mathrm{i}}$ in kelvin and the final temperature is $\mathrm{xT}_{\mathrm{i}}$ in kelvin. The value of $x$ is

The coefficient of mutual induction is 2 H and induced e.m.f. across secondary is 2 kV . Current in the primary is reduced from 6 A to 3 A . The time required for the change of current is

A liquid drop having surface energy $E$ is spread into 729 droplets of same size. The final surface energy of the droplets is

A body is projected vertically from earth's surface with $\left(\frac{1}{3}\right)^{\mathrm{rd}}$ of escape velocity. The maximum height reached by the body is ( $R=$ radius of earth)