At a point very near to the earth's surface, the acceleration due to gravity is g. What will be the acceleration due to gravity at the same point if the earth suddenly shrinks to half its radius without any change in its mass?

A body is taken to a height of $nR$ from the surface of the earth. The ratio of the acceleration due to gravity on the surface to that at the altitude is

At what height from the ground will be the value of $g$ be the same as

that in $10 km$ deep mine below the surface of earth.

Gravity meters measures in units of mGal where 1 Gal (or 1 galileo) is the C.G.S unit of acceleration due to gravity. A gravity meter shows a reading of +300 mGal at a place where the normal 'g' is 9.78 $m s^{-2}$. The correct 'g' at that place where the reading was taken is _____ $m s^{-2}$.