A planet $\left({P}_{1}\right)$ is moving around the star of mass 2M in the orbit of radius R. Another planet $\left({P}_{2}\right)$ is moving around another star of mass 4 M in a orbit of radius 2 R . Ratio of time periods of revolution of ${P}_{2}$ and ${P}_{1}$ is_________ [JEE Main 2026, 2 Apr (Shift 1)]

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YESPYQ · Accepted Answer

Correct answer: b) 2. Using Kepler’s third law: $T\propto \frac{{R}^{3/2}}{\sqrt{M}}$ For ${P}_{1}:{T}_{1}\propto \frac{{R}^{3/2}}{\sqrt{2M}}$ For ${P}_{2}:{T}_{2}\propto \frac{(2R{)}^{3/2}}{\sqrt{4M}}=\frac{\sqrt{2}{R}^{3/2}}{\sqrt{M}}$ Ratio: $\frac{{T}_{2}}{{T}_{1}}=\frac{\sqrt{2}/\sqrt{M}}{1/\sqrt{2M}}=2$

A planet \(\left({P}_{1}\right)\) is moving around the star of mass 2M in the orbit of radius R. Another planet \(\left(…

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