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. `(mg R)/(11 G)`
D. `(10 GMm)/(11 R)`

Answer

D

Explanation

PE at the earth surface = `(- GM m)/(R)`
PE at a length h above the earth 's surface
=` (-GMm)/((R + h))`
`therefore ` Change in PE = `(-GMm)/((R + h)) - (- (GMm)/(R)) = (GMmh)/(R( R + h))`
Substituting h = 10 R
`Delta PE = (GMm xx 10 R)/(R(R + 10 R)) = (10 GMm)/(11R)`