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

\frac{G M m}{12 R^{2}}

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\frac{G M m}{3 R^{2}}

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\frac{G M m}{8 R}

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\frac{G M m}{8 R}

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Solution

The correct option is D $\frac{G M m}{8 R}$
$G r a v i t a t i o n a l P . E = - \frac{G M m}{r} A t r = 2 R; E_{1} = - \frac{G M m}{2 R} A t r = 3 R; E_{2} = - \frac{G M m}{3 R} ∴ E_{2} - E_{1} = - \frac{G M m}{3 R} - (- \frac{G M m}{2 R}) ∴ Δ E = \frac{G M m}{R} (\frac{1}{2} - \frac{1}{3}) Δ E = \frac{G M m}{6 R}$

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

m

2 R

3 R

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