$A$ body weighs $63 \; N$ on the surface of the earth. What is the gravitational force (in $N$) on it due to the earth at a height equal to half the radius of the earth?

The acceleration due to gravity on the Moon is $\frac{1}{6}$ times that of the Earth. If the ratio of the density of the Earth $(\rho_e)$ to the Moon $(\rho_m)$ is $\frac{\rho_e}{\rho_m} = \frac{5}{3}$,what is the radius of the Moon $(R_m)$ in terms of the radius of the Earth $(R_e)$?

As we go from the equator of the earth to the pole of the earth,the value of acceleration due to gravity

Which graph correctly represents the variation of acceleration due to gravity $(g)$ with radial distance $(r)$ from the centre of the earth (radius of the earth $= R_e$)?

If the earth suddenly shrinks (without changing mass) to half of its present radius,the acceleration due to gravity will be

Imagine Earth to be a solid sphere of mass $M$ and radius $R$. If the value of acceleration due to gravity at a depth $d$ below Earth's surface is the same as its value at a height $h$ above its surface and equal to $\frac{g}{4}$ (where $g$ is the value of acceleration due to gravity on the surface of Earth),the ratio of $\frac{h}{d}$ will be