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Q.

Two planets move around the sun. The periodic times and the mean radii of the orbits are $T_{1}, T_{2}$ and $r_{1}, r_{2}$ respectively. The ratio $T_{1} / T_{2}$ is equal to

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a

${(r_{1} / r_{2})}^{3 / 2}$

b

${(r_{1} / r_{2})}^{1 / 2}$

c

${(r_{1} / r_{2})}^{2}$

d

$r_{1} / r_{2}$

answer is D.

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Detailed Solution

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$T^{2} \propto r^{3} \Rightarrow \frac{T_{1}}{T_{2}} = {(\frac{r_{1}}{r_{2}})}^{3 / 2}$

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