A planet ( P₁) is moving around the star of mass 2M in the orbit of radius R. Another planet ( P₂) is moving around another star of mass 4M in a orbit of radius 2R. Ratio of time periods of revolution of P₂ and P₁ is ________. (a) 1/2 (b) 2 (c) 4 (d) 1/4

Answer: (b). Kepler's third law with star mass: T² = (4π² r³)/(GM), so T ∝ √(r³/M). (T₂)/(T₁) = √(((2R)³/(4M))/(R³/(2M))) = √((8 × 2)/(4)) = √(4) = 2 So the answer is (b) 2.

A planet ( P₁) is moving around the star of mass 2M in the orbit of… | JEE Main 2026 (2 Apr, Shift 1)

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Kepler's Laws & Planetary Motion

A planet ( $P_1$ ) is moving around the star of mass $2M$ in the orbit of radius $R$ . Another planet ( $P_2$ ) is moving around another star of mass $4M$ in a orbit of radius $2R$ . Ratio of time periods of revolution of $P_2$ and $P_1$ is ________.

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Answer: (b)

Kepler's third law with star mass: $T^2 = \frac{4\pi^2 r^3}{GM}$ , so $T \propto \sqrt{\frac{r^3}{M}}$ .
$\frac{T_2}{T_1} = \sqrt{\frac{(2R)^3/(4M)}{R^3/(2M)}} = \sqrt{\frac{8 \times 2}{4}} = \sqrt{4} = 2$
So the answer is (b) $2$ .

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