2002 AIPMT GravitationGravitational Potential Energy Medium Question 4 of 5 in Gravitational Potential Energy

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

A $\dfrac{mgR}{4}$
B $\dfrac{2}{3}mgR$
C $\dfrac{3}{4}mgR$
D $\dfrac{mgR}{2}$

The answer is C.

Solution

Gravitational potential energy at distance r from the earth's centre: $U = -\dfrac{GMm}{r}$
Initial (on the surface, r = R): $U_i = -\dfrac{GMm}{R}$
Final (h = 3R, so r = R + 3R = 4R): $U_f = -\dfrac{GMm}{4R}$
Change in GPE $= U_f - U_i = -\dfrac{GMm}{4R} + \dfrac{GMm}{R} = \dfrac{GMm}{R}\left(1 - \dfrac{1}{4}\right)$
$= \dfrac{3}{4}\dfrac{GMm}{R} = \dfrac{3}{4}\dfrac{GM}{R^2}mR = \dfrac{3}{4}mgR$ (since $g = \dfrac{GM}{R^2}$)
(The formula mgh cannot be used, because h is not small compared with R.)

Concept Change in PE for large heights

Gravitational Potential Energy in past papers

5 questions from this chapter have appeared across 4 exam years.