The acceleration due to gravity at the pole $(g_p)$ and at the equator $(g_e)$ are related as:

The mass of the moon is $7.34 \times 10^{22} \ kg$ and the radius of the moon is $1.74 \times 10^6 \ m$. The value of gravitational acceleration on the moon will be ....... $N/kg$.

$A$ 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,

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.

At what height from the ground will the value of $g$ be the same as that in a $10 \, km$ deep mine below the surface of the Earth?

If the radius of the earth is increased by a factor of $5$,by what factor must its density be changed to keep the value of $g$ the same?