A body of mass m is placed on Earth surface which is taken from Earth surface to a height h = 3R, then change in gravitaional potential energy is:

Options

A. `(1)/(4)mgR`
B. `(2)/(3)mgR`
C. `(3)/(4)mgR`
D. `(1)/(2)mgR`

Answer

C

Explanation

Initial gravitational `P.E=-(GMm)/(R)`
Final gravitational `P.E=-(GMm)/((3R+R))=-(GMm)/(4R)`
Change in gravitational `P.E=-(GMm)/(4F)-(-(GMm)/(R))`
`=(3)/(4)(GMm)/(R)=(3GMm)/(4R^2)xxR`
`=(3)/(4)mgR[becauseg=(GM)/(R^2)]`