At a certain depth "$d$" below surface of earth. value of acceleration due to gravity becomes four times that of its value at a height $3\,R$ above earth surface. Where $R$ is Radius of earth (Take $R =6400\,km$ ). The depth $d$ is equal to $............\,km$

At what altitude in metre will the acceleration due to gravity be $25\%$ of that at the earth's surface (Radius of earth $= R\, metre$)

$Assertion$ : An astronaut experience weightlessness in a space satellite.

$Reason$ : When a body falls freely it does not experience gravity

If the value of g at the surface of the earth is $9.8$ $m/{\sec ^2}$, then the value of g at a place $480\, km$ above the surface of the earth will be .......... $m/{\sec ^2}$. (Radius of the earth is $6400\, km$)   

Assuming earth to be a sphere of a uniform density, what is the value of gravitational acceleration in a mine $100\, km$ below the earth’s surface ........ $m/{s^2}$. (Given $R = 6400 \,km$)

The acceleration due to gravity on the earth's surface at the poles is $g$ and angular velocity of the earth about the axis passing through the pole is $\omega .$ An object is weighed at the equator and at a height $h$ above the poles by using a spring balance. If the weights are found to be same, then $h$ is $:( h << R ,$ where $R$ is the radius of the earth)