The work done to raise a mass `m` from the surface of the earth to a height `h`, which is equal to the radius of the earth, is :

Options

A. `3/2 mg R`
B. `mgR`
C. `2mgR`
D. `1/2 mgR`

Answer

D

Explanation

Work done = Change in potential energy
`- u_f -u_i =(-GMm)/((R + h)) - ((-GMm)/(R ))`
where M is the mass of earth and R is the radius of earth.
` therefore W = GMm [1/R - (1)/((R + h))]`
Now, h = R
` therefore W = GMm [ 1/R - (1)/(2R) ] = (GMm)/(2R)`
` rArr W = (mgR)/(2) " " [ because g = (GM)/(R^2) ]`