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>> $If g is acceleration due to gravity on t$

Question

If $g$ is acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is:

A

$2 m g R$

B

$m g R$

C

$\frac{m g R}{4}$

D

$\frac{m g R}{2}$

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Updated on : 2022-09-05

Solution

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Correct option is D)

Value of g is given by: $g = \frac{G M _{e}}{R ^{2}}$
Initial Potential Energy: $U_{i} = - \frac{G M _{e} m}{R} = - M g R$
Final Potential Energy: $U_{f} = - \frac{G M _{e} m}{2 R} = - M g R / 2$
Therefore Gain in Potential Energy: $U_{f} - U_{i} = - M g R / 2 - (- M g R) = \frac{M g R}{2}$

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