Assuming the Earth to be a sphere of uniform mass density,the weight of a body at a depth $d = R/2$ from the surface of the Earth,if its weight on the surface of the Earth is $200 \, N$,will be $........... \, N$ (Given $R =$ Radius of Earth).

The mass of the moon is $(1/8)$ of the earth,but the gravitational pull is $(1/6)$ of the earth. This is due to the fact that:

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 $(R_e)$?

The value of gravitational acceleration $g'$ at a height $h$ above the earth's surface is $\frac{g}{4}$. Then,what is the value of $h$ in terms of the earth's radius $R$?

$Assertion$ : $A$ tennis ball bounces higher on hills than in plains.
$Reason$ : Acceleration due to gravity on the hill is greater than that on the surface of earth.

At what height above the earth's surface is the value of $g$ the same as in a $200 \ km$ deep mine?