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A planet is at R distance from sun and its time period of revolution is T. What will be its new time period of revolution if it is brought 0.5 R distance closer to sun?

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$\frac{4 T}{\sqrt{2}}$

$\frac{\sqrt{2} T}{4}$

$2 \sqrt{2} T$

$\sqrt{2} T$

answer is B.

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Detailed Solution

$\frac{T_{1}^{2}}{T_{2}^{2}} = \frac{R_{1}^{3}}{R_{2}^{2}} ∴ \frac{T^{2}}{T_{2}^{2}} = \frac{R_{1}^{3}}{{(0.5 R_{1})}^{3}}$

$\frac{T}{T_{2}} = \frac{2 \sqrt{2}}{1} T_{2} = \frac{T}{2 \sqrt{2}} = \frac{\sqrt{2} T}{4}$

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