An artificial satellite moving in circular orbit around the earth has a total $($ kinetic + potential $)$ energy $E_{0}$ . Its potential energy and kinetic energy respectively are

2 E_{0}

and

- 2 E_{0}

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2 E_{0}

and

3 E_{0}

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2 E_{0}

and

- E_{0}

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- 2 E_{0}

and

- E_{0}

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Solution

The correct option is C $2 E_{0}$ and $- E_{0}$
From the options itself it is clear that only in option C, when you add PE and KE i.e $2 E_{o} + (- E_{o})$ we get $E_{o}$
Now
Total energy $E_{o} = P . E + K . E = \frac{- G M m}{R} + \frac{1}{2} m v^{2}$
When we substitute $v = \sqrt{\frac{G M}{R}}$ in K.E, we have $K . E = \frac{G M m}{2 R}$
$∴ \frac{- G M m}{R} + \frac{G M m}{2 R} = E_{o}$
$\Rightarrow \frac{- G M m}{R} = 2 E_{o}$
So, $P . E = \frac{- G M m}{R} = 2 E_{o}$ and $K . E = \frac{G M m}{2 R} = - E_{o}$

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E_{0}

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An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential)energy $E_{o}$ . Its potential energy is

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