If the Earth suddenly stops rotating,then the weight of an object of mass $m$ at the equator will $[\omega$ is the angular speed of the Earth and $R$ is its radius]

What is the gravitational force on a particle at the centre of the Earth?

The value of gravitational acceleration $g'$ at a height $h$ above the earth's surface is $\frac{g}{4}$. Then,what is the value of $h$ in terms of the earth's radius $R$?

The acceleration due to gravity is $g$ at a point distant $r$ from the centre of the Earth of radius $R$. If $r < R$,then:

The acceleration due to gravity on the moon is $\frac{1}{6}$ times the acceleration due to gravity on the earth. If the ratio of the density of the earth $\rho_e$ to the density of the moon $\rho_m$ is $\frac{5}{3}$,then the radius of the moon $R_m$ in terms of the radius of the earth $R_e$ is:

Assertion $(A)$: $A$ particle of mass $m$ dropped into a hole made along the diameter of the Earth from one end to the other possesses simple harmonic motion.
Reason $(R)$: Gravitational force between any two particles is inversely proportional to the square of the distance between them.