Assuming the earth to be a sphere of uniform density,the acceleration due to gravity inside the earth at a distance of $r$ from the centre is proportional to

The radius of the Earth is about $6400 \; km$ and that of Mars is $3200 \; km$. The mass of the Earth is about $10$ times the mass of Mars. An object weighs $200 \; N$ on the surface of the Earth. Its weight on the surface of Mars will be .......... $N$.

If the earth were to cease rotating about its own axis,the increase in the value of $g$ in the $C.G.S.$ system at a place of latitude of $45^{\circ}$ will be ........ $cm/sec^{2}$.

The diameters of two planets are in the ratio $4:1$. Their mean densities have the ratio $1:2$. The ratio of gravitational acceleration on the surface of the planets will be:

What is the depth at which the value of acceleration due to gravity becomes $\frac{1}{n}$ times the value at the surface of the Earth? (radius of Earth $= R$)

$A$ body weighs $45 \ N$ on the surface of the earth. The gravitational force on a body due to the earth at a height equal to half the radius of the earth will be: (in $N$)