$A$ body thrown on Earth reaches a height of $90\,m$. If the same body is thrown on a planet with $\frac{1}{10}$ of the mass and $\frac{1}{3}$ of the radius of Earth,it will reach a height of ....... $m$.

The height of any point $P$ above the surface of the Earth is equal to the diameter of the Earth. The value of acceleration due to gravity at point $P$ will be: (Given $g = $ acceleration due to gravity at the surface of the Earth)

Calculate the difference in the value of $g$ at the equator and at the poles due to the rotation of the Earth.

Starting from the centre of the earth having radius $R$,the variation of $g$ (acceleration due to gravity) is shown by:

In the provided figure of the Earth,the value of acceleration due to gravity is the same at points $A$ and $C$,but it is smaller than its value at point $B$ (surface of the Earth). The value of $OA : AB$ is $x : y$. The value of $x$ is $\ldots \ldots \ldots$

$A$ pendulum is oscillating with frequency $n$ on the surface of the Earth. If it is taken to a depth $d = R/3$ below the surface of the Earth,what is the new frequency of oscillation? ($R$ is the radius of the Earth)