The average density of the Earth is [ $g$ is acceleration due to gravity]:

The radii of two planets $A$ and $B$ are $R$ and $4R$ and their densities are $\rho$ and $\rho/3$ respectively. The ratio of acceleration due to gravity at their surfaces $(g_A : g_B)$ will be

The acceleration due to gravity at a height of $(\sqrt{2}-1) R$ from the surface of the earth is (Acceleration due to gravity on the surface of the earth $= 10 \ m \ s^{-2}$ and $R$ is radius of the earth). (in $m \ s^{-2}$)

The weight of a body on the earth is $400\,N$. Then weight of the body when taken to a depth half of the radius of the earth will be ............ $N$.

The mass of a planet is $\frac{1}{9}$ of the mass of the Earth and its radius is half that of the Earth. If a body weighs $9 \ N$ on the Earth,its weight on the planet would be ........ $N$.

$A$ body weighs $63 \; N$ on the surface of the earth. What is the gravitational force (in $N$) on it due to the earth at a height equal to half the radius of the earth?