A body of mass $m$ is taken to the bottom of a deep mine. Then

If ${R}_{{E}}$ be the radius of Earth, then the ratio between the acceleration due to gravity at a depth $' {r} '$ below and a height $' r '$ above the earth surface is:

(Given : $\left.{r}<{R}_{{E}}\right)$

A particle is dropped on Earth from height $R$ (radius of Earth) and it bounces back to a height $R/2$ the coefficient of restitution for collision is (ignore air resistance and rotation of Earth)

Given below are two statements :

Statement$-I:$ Acceleration due to gravity is different at different places on the surface of earth.

Statement$-II:$ Acceleration due to gravity increases as we go down below the earth's surface.

In the light of the above statements, choose the correct answer from the options given below

The radii of two planets $A$ and $B$ are $R$ and $4 R$ and their densities are $\rho$ and $\rho / 3$ respectively. The ratio of acceleration due to gravity at their surfaces $\left(g_A: g_B\right)$ will be

Choose the correct statement from the following :Weightlessness of an astronaut moving in a satellite is a situation of