In a satellite, if the time of revolution is $T$ , then KE is proportional to.

\frac{1}{T}

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\frac{1}{T^{2}}

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\frac{1}{T^{3}}

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T^{- 2 / 3}

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Solution

The correct option is B $T^{- 2 / 3}$
Velocity of satellite $v = \sqrt{\frac{G M}{r}}$
$∴ K E \propto v^{2} \propto \frac{1}{r}$ and $T^{2} \propto r^{3}$
$∴ K E \propto T^{- 2 / 3}$

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