First slide

Gravitaional potential energy

Question

A satellite is moving in a circular orbit of radius $r$ around earth with kinetic energy K. What work is to be done on the satellite to stop the satellite at any position in its orbit

Moderate

A

$\frac{K}{2}$
B

$- \frac{K}{2}$
C

K
D

-K

Solution

Total energy of the satellite $= - K = - \frac{G M m}{2 r}$
After the satellite is stopped, its total energy will be equal to its potential energy $U = - \frac{G M m}{r} = - 2 K$
$∴$ Work done = Final total energy - Initial total energy $= - 2 K - (- K) = - K$

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