Two planets are revolving around the Earth with velocities $v_{1}, v_{2}$ and in radii $r_{1}$ and $r_{2}$ ( $r_{1} > r_{2}$ ) respectively. Then

v_{1} = v_{2}

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v_{1} > v_{2}

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v_{1} < v_{2}

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\frac{v_{1}}{r_{1}} = \frac{v_{2}}{r_{2}}

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Solution

The correct option is D $v_{1} < v_{2}$
$v_{0} = \sqrt{\frac{G M}{r}}$
$∴ \frac{v_{1}}{v_{2}} = \sqrt{\frac{r_{2}}{r_{1}}}$
$∵ r_{1} > r_{2} ∴ v_{2} > v_{1}$

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