The weight of a body at the centre of the earth is

The acceleration due to gravity on the Moon is $\frac{1}{6}$ times that of the Earth. If the ratio of the density of the Earth $(\rho_e)$ to the Moon $(\rho_m)$ is $\frac{\rho_e}{\rho_m} = \frac{5}{3}$,what is the radius of the Moon $(R_m)$ in terms of the radius of the Earth $(R_e)$?

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R).$
Assertion $(A):$ Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
Reason $(R):$ Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.
In the light of the above statements,choose the most appropriate answer from the options given below:

The period of oscillation of a simple pendulum of constant length at the Earth's surface is $T$. Its period inside a mine is

The value of acceleration due to gravity at a depth $d$ from the surface of the Earth and at an altitude $h$ from the surface of the Earth are in the ratio:

How can we conclude that the Earth is not a perfect sphere based on the acceleration due to gravity?