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Gravitational Potential Energy

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Question

Find the work done to take a particle of mass m from surface of the earth to a height equal to $2 R$ .

A

2

m g R

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B

\frac{m g R}{2}

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C

3 m g R

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D

\frac{2 m g R}{3}

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Solution

The correct option is D $\frac{2 m g R}{3}$
$W o r k D o n e = Δ P E P E = \frac{G M m}{r} Δ P E = G M m (\frac{1}{R} - \frac{1}{3 R}) = \frac{2 G M m}{3 R} = \frac{2}{3} m g R$

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