If the acceleration due to gravity at the surface of the earth is g, the work done is slowly lifting a body of mass in from the earth's surface to a height R equal to the radius of the earth is

Explanation

Let `W_(ex)` be the required work done in this case.
`W_(ex) = Delta U- U_f - U_v`
`U_f = - (GMm)/((2R)) , U_0 = - (GMm)/( R)`
`Delta U = - (GMm)/(2R) + (GMm)/(R ) = (GMm)/(2R)`
Now , ` mg = (GMm)/(R^2) " or " g = (GM)/(R^2) rArr Delta U = (mg R)/(2)`
` rArr W_(ex) = (mg R)/(2)`