The depth at which the effective value of acceleration due to gravity is $\frac{g}{4}$ is

$A$ narrow but tall cabin is falling freely near the earth's surface. Inside the cabin,two small stones $A$ and $B$ are released from rest (relative to the cabin). Initially $A$ is much above the centre of mass and $B$ is much below the centre of mass of the cabin. $A$ close observation of the motion of $A$ and $B$ will reveal that

The mass of the moon is $\frac{1}{81}$ of the earth,but the gravitational pull (acceleration due to gravity) is $\frac{1}{6}$ of the earth. This is due to the fact that:

As we move from the poles of the Earth towards the equator,what happens to the value of the acceleration due to gravity $(g)$?

The acceleration due to gravity at an altitude $h$ above the Earth's surface is half of its value on the surface of the Earth. If the radius of the Earth $R = 4000 \ mile$,the altitude $h$ is approximately ......... $mile$.

$A$ uniform solid sphere of radius $R$ produces a gravitational acceleration of $a_o$ on its surface. The distance of the point from the centre of the sphere where the gravitational acceleration becomes $\frac{a_o}{4}$ is,