$A$ body weighs $72 \ N$ on the surface of the earth. What is the gravitational force on it at a height equal to half the radius of the earth (in $N$)?

The mass of the moon is $7.34 \times 10^{22} \ kg$. If the acceleration due to gravity on the moon is $1.4 \ m/s^2$,calculate the radius of the moon. (Given: $G = 6.667 \times 10^{-11} \ N \cdot m^2/kg^2$)

The maximum vertical distance through which a fully dressed astronaut can jump on the earth is $0.5\, m$. If the mean density of the moon is two-thirds that of the earth and the radius is one-quarter that of the earth,what is the maximum vertical distance through which he can jump on the moon and the ratio of the duration of the jump on the moon to that on the earth?

The distance through which one has to dig the earth from its surface so as to reach the point where the acceleration due to gravity is reduced by $40 \%$ of that at the surface of the earth,is (radius of earth is $6400 \ km$) (in $km$)

State the values of $g$ and $G$ at the center of the Earth. Identify which of $g$ and $G$ is a vector and which is a scalar.

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