A satellite revolves in the geostationary orbit but in a direction east to west. The time interval between its successive passing about a point on the equator is …….. $hrs$

A body weighs $700\, gm$ weight on the surface of the earth. How much will it weigh on the surface of a planet whose mass is $\frac{1}{7}$ and radius is half that of the earth …… $gm\, wt$

Mass density of a solid sphere is $\rho $ . Radius of the sphere is $R$. The gravitational field at a distance $r$ from the centre of the sphere inside it is

The rotation of the earth having radius $R$ about its axis speeds upto a value such that a man at latitude angle $60^{\circ}$ feels weightless. The duration of the day in such case will be:

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