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Question: Energy required to move a body of mass m from an orbit of radius \(3 R\) is...

Energy required to move a body of mass m from an orbit of radius 3R3 R is

A

GMm12R2\frac { G M m } { 12 R ^ { 2 } }

B

GMm3R2\frac { G M m } { 3 R ^ { 2 } }

C

GMm8R\frac { G M m } { 8 R }

D

GMm6R\frac { G M m } { 6 R }

Answer

GMm6R\frac { G M m } { 6 R }

Explanation

Solution

Work done = Change in potential energy =U2−U1= U _ { 2 } - U _ { 1 } =[−GMmr2]−[−GMmr1]= \left[ - \frac { G M m } { r _ { 2 } } \right] - \left[ - \frac { G M m } { r _ { 1 } } \right] =GMm6R= \frac { G M m } { 6 R }.