$A$ hole is drilled through the Earth along a diameter and a stone is dropped into it. When the stone reaches the center of the Earth,which of the following quantities remains constant?

If the Earth has no rotational motion,the weight of a person on the equator is $W$. Determine the speed with which the Earth would have to rotate about its axis so that the person at the equator will weigh $\frac{3}{4} W$. The radius of the Earth is $6400 \ km$ and $g = 10 \ m/s^2$.

What is the effect on the value of $g$ at the equator if the Earth stops its rotation?

$A$ pendulum is oscillating with frequency $n$ on the surface of the Earth. If it is taken to a depth $d = \frac{R}{2}$ below the surface of the Earth,where $R$ is the radius of the Earth,what is the new frequency of oscillations at this depth?

$A$ simple pendulum is taken from the equator to the pole. Its period

$A$ body weighs $72 \, N$ on the surface of the earth. When it is taken to a height of $h = 2R$,where $R$ is the radius of the earth,it would weigh ........ $N$.