Question

# 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 :

A
mgR
B
2 mgR
C
12mgR
D
32mgR

Solution

## The correct option is C $$\dfrac{1}{2} mgR$$Initial potential energy at earths surface is $$U_i = \dfrac{-GMm}{R}$$Final potential energy at height h = R$$U_f = \dfrac{-GMm}{2R}$$As work done = change in PE$$\therefore W = U_f - U_i$$$$= \dfrac{GMm}{2R}$$$$(\because GM = gR^2)$$$$= \dfrac{gR^2m}{2R} = \dfrac{mgR}{2}$$     Physics

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