The height $h$ above the earth's surface at which the value of acceleration due to gravity $g$ becomes $\frac{g}{3}$ is ($R=$ radius of the earth).

If the acceleration due to gravity at the Earth is $g$,the mass of the Earth is $80$ times that of the Moon,and the radius of the Earth is $4$ times that of the Moon,then the value of the acceleration due to gravity at the surface of the Moon will be:

The acceleration due to gravity on a planet is $1.96 \, m/s^2$. If it is safe to jump from a height of $3 \, m$ on the Earth,the corresponding height on the planet will be ........ $m$.

The value of the acceleration due to gravity is $g_{1}$ at a height $h = \frac{R}{2}$ ($R$ = radius of the earth) from the surface of the earth. It is again equal to $g_{1}$ at a depth $d$ below the surface of the earth. The ratio $\left(\frac{d}{R}\right)$ equals

If the radius of the earth shrinks by $1.5\%$ (mass remaining same),then the value of acceleration due to gravity changes by ....... $\%$.

The weight of a body on the surface of the earth is $100\,N$. The gravitational force on it when taken at a height,from the surface of earth,equal to one-fourth the radius of the earth is $..........\,N$.