A body of mass `m` rises to a height `h=R//5` from the earth's surface where `R` is earth's radius. If `g` is acceleration due to gravity at the earth's surface, the increase in potential energy is

Options

A. `mgh`
B. `4/5mgh`
C. `5/6mgh`
D. `6/7mgh`

Answer

C

Explanation

Increases in gravitational potential energy
`=[-(GMm)/(R+R/5)]-[-(GMm)/R]`
`=(GMm)/R-(GMmxx5)/(6R)`
`=(GMm)/R[1-5/6]=(GMm)/Rxx1/6`
`=(mgR^(2))/(6R)=1/6mgR=5/6mgh.[ :'R=5h]`