A body of mass `m` is raised to a height 10 R from the surface of the earth, where R is the radius of the earth. Find the increase in potential energy. (G = universal constant of gravitational, M = mass of the earth and g= acceleration due to gravity)

Options

A. `(GMm)/(11R)`
B. `(GMm)/(10R)`
C. `(mgR)/(11G)`
D. `(10GMm)/(11R)`

Answer

D

Explanation

At the surface of the earth, gravitational P.E.
`U_(1)=-(GMm)/(R )`
at a height `h = R + 10R = 11R`
`U_(2)=-(GMm)/(11R)`
`therefore U_(2)-U_(1)=-(GMm)/(11R)+(GMm)/(R )`
`=(GMm)/(R )[1-(1)/(11)]`
`=+(10)/(11)(GMm)/(R )`