The height of the point vertically above the earth’s surface, at which acceleration due to gravity becomes $1\%$ of its value at the surface is (Radius of the earth $= R$)

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

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 $6400\, km$.

A person whose mass is $100\, {kg}$ travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as $10$ ${m} / {s}^{2}$ and $4 \,{m} / {s}^{2}$ respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.

In order to find time, the astronaut orbiting in an earth satellite should use

Spot the wrong statement :The acceleration due to gravity $‘g’$ decreases if