The acceleration due to gravity on the surface of the earth is g. If a body of mass m is raised from the surface of the earth to a height equal to the radius R of the earth, then the gain in its potential energy is given by

Options

A. mgR
B. 2 mgR
C. `(1)/(2) mgR`
D. `(1)/(4)mgR`

Answer

C

Explanation

P.E. on the surface `=-(GMm)/(R )`
P.E. at a height `h =R =-(GMm)/(R+R)`
`therefore` Gain in P.E. `=-(GMm)/(2R)+(GMm)/(R )=(GMm)/(2R)`
But `GM=gR^(2)therefore` Gain `=(gR^(2)m)/(2R)=(1)/(2)gmR`