$A$ body weighs $500 \,N$ on the surface of the earth. At what distance below the surface of the earth will it weigh $250 \,N$ (in $\,km$)? (Radius of earth, $R = 6400 \,km$)

Obtain the general equation of gravitational force at a distance $r$ from the centre of the Earth and derive the equation for acceleration due to gravity on the surface of the Earth.

The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is $2 \ s$. The period of oscillation of the same pendulum on the planet would be

$A$ body has weight $W$ newton at the surface of the earth. Its weight at a height equal to half the radius of the earth will be:

Calculate the difference in the value of $g$ at the equator and at the poles due to the rotation of the Earth.

If the mass of the Earth decreases by $25 \%$ and its radius increases by $50 \%$,then the acceleration due to gravity at its surface decreases by nearly ......... $\%$