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

$A$ hole is drilled halfway to the center of the Earth. $A$ body weighs $300 \ N$ on the surface of the Earth. How much will it weigh at the bottom of the hole (in $N$)?

What effect occurs on the frequency of a pendulum if it is taken from the earth's surface to deep into a mine?

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating,the duration of the day would be approximately ........ minutes
(Take: $g = 10 \, m/s^2$,the radius of earth,$R = 6400 \times 10^3 \, m$,Take $\pi = 3.14$)

If $g_E$ and $g_M$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces,one will find the ratio (electronic charge on the moon / electronic charge on the earth) to be

If the Earth is assumed to be a sphere of radius $R$,and $g_{30}$ is the value of acceleration due to gravity at a latitude of $30^\circ$ and $g$ is the value at the equator,the value of $g - g_{30}$ is: