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

Answer

D

Explanation

Potential energy at the earth surface `= (-GMm)/(R)`
Potential energy at a height h above the earth's surface
`= (-GMm)/((R+h))`
`:.` Change in potential energy `= (-GMm)/((R+h))-(-(Gmm)/(R))`
`=(GMmh)/(R(R+h))`
Substituting, h = 10 R
`rArr DeltaPE=(GMmxx10R)/(R(R+10R))=(10GMm)/(11R)`.