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

The ratio of the accelerations due to gravity at heights $1280 \ km$ and $3200 \ km$ above the surface of the earth is (Radius of the earth $= 6400 \ km$)

Considering Earth to be a sphere of radius $R$ having uniform density $\rho$,the value of acceleration due to gravity $g$ in terms of $R$,$\rho$,and $G$ is:

The magnitudes of the gravitational field at distances $r_1$ and $r_2$ from the center of a uniform sphere of radius $R$ and mass $M$ are $F_1$ and $F_2$ respectively. Then:

If the acceleration due to gravity experienced by a point mass at a height $h$ above the surface of the Earth is the same as the acceleration due to gravity at a depth $d = \alpha h$ $(h \ll R_{e})$ from the Earth's surface,then the value of $\alpha$ will be: (use $R_{e} = 6400 \ km$)

If the earth stops rotating,the value of $g$ at the equator will