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(D) The total mechanical energy $(E)$ of a satellite is the sum of its kinetic energy $(K.E.)$ and potential energy $(U)$.The gravitational potential

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$-\frac{GMm}{2r}$

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(D) The total mechanical energy $(E)$ of a satellite is the sum of its kinetic energy $(K.E.)$ and potential energy $(U)$.The gravitational potential energy of a satellite of mass $m$ at a distance $r$ from the centre of the Earth (mass $M$) is given by $U = -\frac{GMm}{r}$.For a satellite in a circular orbit,the centripetal force is provided by the gravitational force:$\frac{mv^2}{r} = \frac{GMm}{r^2} \implies mv^2 = \frac{GMm}{r}$.The kinetic energy is $K.E. = \frac{1}{2}mv^2 = \frac{1}{2} \left( \frac{GMm}{r} \right) = \frac{GMm}{2r}$.The total mechanical energy is $E = K.E. + U = \frac{GMm}{2r} - \frac{GMm}{r} = -\frac{GMm}{2r}$.

$A$ satellite of mass $m$ is placed at a distance $r$ from the centre of the Earth (mass $M$). The mechanical energy of the satellite is

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