If the mass of the Earth is M,its radius is R | vedclass

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(B) The gravitational potential energy $U$ of a mass $m$ at a distance $r$ from the center of the Earth is given by $U = -\frac{GMm}{r}$.At the surfac

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$\frac{GM}{R}$

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(B) The gravitational potential energy $U$ of a mass $m$ at a distance $r$ from the center of the Earth is given by $U = -\frac{GMm}{r}$.At the surface of the Earth,$r = R$ and $m = 1 \, kg$,so the initial potential energy is $U_i = -\frac{GM(1)}{R} = -\frac{GM}{R}$.At infinity,the distance $r = \infty$,so the final potential energy is $U_f = -\frac{GM(1)}{\infty} = 0$.The work done $W$ is equal to the change in potential energy: $W = U_f - U_i$.$W = 0 - (-\frac{GM}{R}) = \frac{GM}{R}$.

If the mass of the Earth is $M$,its radius is $R$,and the gravitational constant is $G$,then the work done to take a $1 \, kg$ mass from the Earth's surface to infinity will be:

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