A body of mass m taken from the earth's surface to the height h = 3R (R = Radius of earth) The change in gravitational potential energy of the body will be ........

Options

A. `2/3 mgR`
B. `3/4 mgR`
C. `(mgR)/2`
D. `(mgR)/4`

Answer

B

Explanation

`implies` One the surface of earth `U_1 = -(GMm)/R`
(R = Radius of earth M = mass of earth)
For height h = 3R form the surface of earth and distance r form the centre of earth
`r = R + h = R + 3R = UR`
`U_2 =-(GMm)/(4R)`
`U_2-U_1 =-(GMm)/(4R)+(GMm)/R`
`=(GMm)/R [-1/4 +1]`
`=(GMm)/R [-(1+4)/4]`
`= (3GMm)/(4R)`
Putting `GM=gR^2`
`U_2 -U_1 = (3gR^2m)/(4R) = 3/4 mgR`