Question

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

• A. $GMm/12R^2$
• B. $GMm/3R^2$
• C. $GMm/8R$
• D. $GMm/6R$

Answer 1

Answer: (D)

Gravitational potential energy of body will be $E=\frac{G{M}_{e}m}{r}$ where $m_e=$ mass of earth, $m=$ mass of the body, $R=$ radius of earth At $r=2R,$ $E_1=-\frac{G{M}_{e}m}{r}$ At $r=2R,$ $E_2=-\frac{G{M}_{e}m}{(3R)}$ Energy required to move a body of mass m from an orbit of radius 2R to 3R is $\Delta E=\frac{G{M}_{e}m}{R}\left[\frac{1}{2}-\frac{1}{3}\right]$ $=\frac{G{M}_{e}m}{6R}$