A body of mass `m` taken form the earth's surface to the height is equal to twice the radius `(R)` of the earth. The change in potential energy of body will be

Options

A. `mgR2`
B. `(2)/(3)mgR`
C. `3mgR`
D. `(1)/(3) mgR`

Answer

B

Explanation

Change in potential energy
`DeltaU=-(GMm)/(R+2R)-(-(GMm)/(R))`
`=-(GMm)/(3R)+(GMm)/(R)=(2GMm)/(3R)=(2)/(3) mgR" "[because g = (GM)/(R^(2))]`.