JEE Main 2002 — Gravitation Question with Solution

Gravitational potential energy E = $$-\frac{GMm}{r}$$

where M = mass of earth

m = mass of body

r = radius of earth

Energy required to move a body of mass $$m$$ from an orbit of radius $$2R$$ to $$3R$$

$$=$$ (Potential energy of the Earth-mass system when mass is at distance $$3R$$ ) $$-$$ (Potential energy of the Earth-mass system when mass is at distance $$2R$$)

$$=\frac{-GMm}{3R}-\left(\frac{-GMm}{2R}\right)$$

$$=\frac{-GMm}{3R}+\frac{GMm}{2R}$$

$$=\frac{-2GMm+3GMm}{6R}=\frac{GMm}{6R}$$