At what height from the ground will the value of $‘g’ $ be the same as that in $10 \,km$ deep mine below the surface of earth ......... $km$

The mass of the moon is $\frac{1}{{81}}$ of the earth but the gravitational pull is $\frac{1}{6}$ of the earth. It is due to the fact that

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion $A:$ A pendulum clock when taken to Mount Everest becomes fast.

Reason $R:$ The value of $g$ (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth.

In the light of the above statements, choose the most appropriate answer from the options given below

Derive the equation for variation of $g$ due to height from the surface of earth.

A body of mass $m$ is taken to the bottom of a deep mine. Then

The radius of the earth is $6400\, km$ and $g = 10\,m/{\sec ^2}$. In order that a body of $5 \,kg$ weighs zero at the equator, the angular speed of the earth is