When a body is taken from the pole to the equator,its weight:

$A$ body weighs $300 \ N$ on the surface of the earth. How much will it weigh at a distance $\frac{R}{2}$ below the surface of the earth (in $N$)? ($R$ is the radius of the earth.)

There is a planet which is $8$ times more massive and $27$ times denser than the Earth. If $g^{\prime}$ and $g$ are the accelerations due to gravity on the surfaces of the planet and the Earth respectively,then:

At what altitude in metres will the acceleration due to gravity be $25\%$ of that at the earth's surface? (Radius of earth $= R \ m$)

How does the rotation of the Earth affect the acceleration due to gravity on its surface?

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