In order to shift a body of mass m from a cir | vedclass

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(B) The total mechanical energy $E$ of a body of mass $m$ in a circular orbit of radius $r$ is given by $E = -\frac{GMm}{2r}$.To shift the body from r

Vedclass · Accepted Answer

$\frac{1}{15} \frac{GMm}{R}$

Vedclass · Answer

(B) The total mechanical energy $E$ of a body of mass $m$ in a circular orbit of radius $r$ is given by $E = -\frac{GMm}{2r}$.To shift the body from radius $r_1 = 3R$ to $r_2 = 5R$,the work done $W$ is equal to the change in mechanical energy: $W = E_2 - E_1$.$W = \left( -\frac{GMm}{2(5R)} \right) - \left( -\frac{GMm}{2(3R)} \right)$.$W = \frac{GMm}{2} \left( \frac{1}{3R} - \frac{1}{5R} \right)$.$W = \frac{GMm}{2} \left( \frac{5 - 3}{15R} \right) = \frac{GMm}{2} \left( \frac{2}{15R} \right) = \frac{1}{15} \frac{GMm}{R}$.

In order to shift a body of mass $m$ from a circular orbit of radius $3R$ to a higher radius $5R$ around the Earth,the work done is:

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