At  ….. $km$ height from the surface of earth the gravitation potential and the value of $g$ are  $-5.4 \times 10^7\, J kg^{-1}$ and $6.0\,m s^{-2}$ respectively . Take the radius of earth as $6400\, km$.

If the acceleration due to gravity experienced by a point mass at a height $h$ above the surface of earth is same as that of the acceleration due to gravity at a depth a depth $\alpha$ h $\left(h \ll R_{e}\right)$ from the earth surface. The value of $\alpha$ will be$….$(use $R _{ e }=6400\,km$ )

If a man at the equator would weigh $(3/5)^{th}$ of his weight, the angular speed of the earth is

If the mass of earth is $80$ times of that of a planet and diameter is double that of planet and $‘g’$ on earth is $9.8\,m/{s^2}$, then the value of $‘g’ $ on that planet is …….. $m/{s^2}$

A simple pendulum has a time period ${T_1}$ when on the earth’s surface and ${T_2}$ when taken to a height $R$ above the earth’s surface, where $R$ is the radius of the earth. The value of ${T_2}/{T_1}$ is