If a man at the equator would weigh $(3/5)^{th}$ of his weight, the angular speed of the earth is

Let $\omega$ be the angular velocity of the earth’s rotation about its axis. Assume that the acceleration due to gravity on the earth’s surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth’s surface at a pole $(d < < R)$ The value of $d$ is

If $M$ the mass of the earth and $R$ its radius, the ratio of the gravitational acceleration and the gravitational constant is

A star of mass $M$ and radius $R$ is made up of gases. The average gravitational pressure compressing the star due to gravitational pull of the gases making up the star depends on $R$ as

The radii of two planets $A$ and $B$ are $R$ and $4 R$ and their densities are $\rho$ and $\rho / 3$ respectively. The ratio of acceleration due to gravity at their surfaces $\left(g_A: g_B\right)$ will be