$A$ 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, $R = 6400 \,km$)

The percentage decrease in the weight of a rocket,when taken to a height of $32 \ km$ above the surface of the Earth,will be $.....\%$
(Radius of Earth $= 6400 \ km$)

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

The value of acceleration due to gravity at a height of $10 \,km$ from the surface of the Earth is $x$. At what depth inside the Earth is the value of the acceleration due to gravity the same value $x$ (in $\,km$)?

The masses of two planets are in the ratio $1 : 2$. Their radii are in the ratio $1 : 2$. The ratio of the acceleration due to gravity on the planets is:

The ratio of the time periods of a simple pendulum at heights $2 R_E$ and $3 R_E$ from the surface of the earth is ($R_E$ is the radius of the earth).