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  4. Suppose to planets A and B revolved around a Sun in the galaxy. The semi major axis of A and B are 1 and 5 AU (astronomical unit) respectively. If the period of revolution of A is 1 year, the period of revolution of B is

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Q. Suppose to planets A and B revolved around a Sun in the galaxy. The semi major axis of A and B are 1 and $5\, AU$ (astronomical unit) respectively. If the period of revolution of A is 1 year, the period of revolution of B is

KEAMKEAM 2019Gravitation

Solution:

Given, semi-major axis of planets, $R_{A}=1\, AU$ and $R_{B}=5\, AU$, and period of revolution of planet $A$,
$T_{A}= 1\, yr.$
As, $\left(\frac{T_{A}}{T_{B}}\right)^{2}=\left(\frac{R_{A}}{R_{B}}\right)^{3}$
$\Rightarrow \left(\frac{1}{T_{B}}\right)^{2}=\left(\frac{1}{5}\right)^{3}$
$\Rightarrow T_{B}=\sqrt{125}=11.18\,yr$