A planet is moving around the star of mass 2M in the orbit of radius R. Another planet is moving around another

Question

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 an orbit of radius 2R. Ratio of time periods of revolution of $P_{2}$ and $P_{1}$ is ______. [2026]

Smart Achievers · Accepted Answer

(2)

$From Kepler's law,$

$T^{2} = \frac{4 π^{2}}{G M_{s}} r^{3}$

$∴$ $T_{P_{1}} = \frac{2 π}{\sqrt{G (2 M)}} R^{3 / 2}$

$T_{P_{2}} = \frac{2 π}{\sqrt{G (4 M)}} {(2 R)}^{3 / 2}$

$∴$ $\frac{T_{P_{2}}}{T_{P_{1}}} = \frac{{(2)}^{3 / 2}}{\sqrt{4}} \times \frac{\sqrt{2}}{1} = \frac{2 \sqrt{2} \times \sqrt{2}}{2} = 2$

Solution

Q.
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 an orbit of radius 2R. Ratio of time periods of revolution of $P_{2}$ and $P_{1}$ is ______. [2026]

1 $\frac{1}{2}$

2 $2$

3 $4$

4 $\frac{1}{4}$

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Solution

Q. 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 an orbit of radius 2R. Ratio of time periods of revolution of P2 and P1 is ______. [2026]

1 12

2 2

3 4

4 14