A small planet is revolving around a very massive star in a circular orbit of radius ' $R$ ' with a period of revolution ' $T$ '. If the gravitational force between the planet and the star were proportional to '$R^{-5 / 2}$', then '$T$' would be proportional to

A metal sphere of radius R, density $\rho_1$ moves with terminal velocity $\mathrm{V}_1$ through a liquid of density $\sigma$. Another sphere of same radius but density $\rho_2$ moves through same liquid. Its terminal velocity is $\mathrm{V}_2$. The ratio $\mathrm{V}_1: \mathrm{V}_2$ is

In the circuit, current flowing through the circuit is

Two point charges +10 q and -4 q are located at $\mathrm{x}=0$ and $\mathrm{x}=\mathrm{L}$ respectively. What is the location of a point on the $x$-axis from the origin, which the net electric field due to these two point charges is zero?( $r=$ required distance$)$