If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth, is

Options

A. mg R/4
B. mg R/2
C. mg R
D. 2 mg R

Answer

b

Explanation

The gain in potential energy is,
`P.E._(2)-P.E._(1)=-(GmM)/(2R)+(GMm)/(R)`
`=(1)/(2)xx(GMm)/(R^(2))xxR`
`=(GM)/(2R^(2))mR=(mgR)/(2)(because R=(GM)/(R^(2)))`
Note that the expression PE = mgh is an approximate one which is valid if `h lt lt R.`