The height from the surface of earth at which the gravitational potential energy of a ball of mass `m` is half of that at the centre of earth is (where `R` is the radius of earth)

Options

A. `(R)/(4)`
B. `(R)/(3)`
C. `(3R)/(4)`
D. `(4R)/(3)`

Answer

B

Explanation

`U = mV`
or `U prop V`
`U` is half, if means gravitational potential is half.
`-(GM)/((R + h)) = (1)/(2) [-(3)/(2) (GM)/(R)]`
Solving we get, `h = (R)/(3)`