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. `(10 GMm)/(11R)`

Answer

D

Explanation

PE at the earth surface `=(-GMm)/(R )`
PE at a height h above the earth surface `=-(-GMm)/(R+h)`
`therefore` change in PE `=-(GMm)/(R+h)-(GMm)/(R )=(GMmh)/(R(R+h))`
subsitituting h=10R
`triangle PE =(GMmxx10R)/(R (R+10R)=(10GMm)/(11R)`