Consider two spherical planets of same average density. Second planet is $8$ times as massive as first planet. The ratio of the acceleration due to gravity of the second planet to that of the first planet is

The acceleration due to gravity at pole and equator can be related as

A planet of radius $R =\frac{1}{10} \times$ (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth $\frac{R}{5}$ on it and lower a wire of the same length and of linear mass density $10^{-3} \ kgm ^{-1}$ into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth $=6 \times 10^6 \ m$ and the acceleration due to gravity on Earth is $10 \ ms ^{-2}$ )

Two planets $A$ and $B$ have same mass and radii $(R)$ . The variation of density of the planets with distance from centre is shown in the following diagrams. The ratio of acceleration due to gravity at the surface of the planets $A$ and $B$ will be

At what distance above and below the surface of the earth a body will have same weight, (take radius of earth as $R$.)

What is value of acceleration due to gravity $(g)$ at the centre of earth ? What will be the variation of $g$ below and above the surface of earth ?