A body of mass `m` is placed on the earth surface is taken to a height of `h=3R`, then, change in gravitational potential energy is

Options

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

Answer

D

Explanation

P.E. of the body of mass 'm' at the surface of the earth is
`U_(E )=-(GMm)/(R )" "` ……(1)
When it is taken to a height h = 3R, then the P.E. is given by
`U_(h)=-(GMm)/(R+h)=-(GMm)/(4R)" "` ……(2)
`therefore` Change in gravitational P.E.
`Delta U = -(GMm)/(4R)-(-(GM)/(R ))=+(3GMm)/(4R)" "` .....(3)
But `GM=gR^(2)`
`therefore Delta U = (3)/(4) mgR" "` ........(4)