The gravitational potential energy of a body at a distance `r` from the centre of earth is `U`. Its weight at a distance `2r` from the centre of earth is

Options

A. `(U)/(r)`
B. `(U)/(2r)`
C. `(U)/(4r)`
D. `(U)/(sqrt2r)`

Answer

C

Explanation

`U = (-GMm)/(R)`
`:. (-GM) = (Ur)/(m)`
`E = - (GM)/((2r)^(2)) = ((Ur//m))/(4r^(2)) = (U)/(4mr)`
`F = mE = (U)/(4r)`