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

Options

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

Answer

C

Explanation

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