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

Question

Energy required to place a body of mass m from an orbit of radius 2R to 3R is (Given that M = mass of earth, R = Radius of Earth)

Smart Achievers · Accepted Answer

(2)

$Δ E = T E (3 R) - T E (2 R)$

$Δ E = - \frac{G M m}{6 R} + \frac{G M m}{4 R} = \frac{G M m}{R} [\frac{1}{4} - \frac{1}{6}]$

$Δ E = \frac{G M m}{R} [\frac{6 - 4}{24}] = \frac{G M m}{12 R}$

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