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PhysicsGravitationSatellite MotionMedium2 minPYQ_2021

PhysicsMediumnumerical

The distance between two stars of masses $3 M_{S}$ and $6 M_{S}$ is $9 R$ . Here $R$ is the mean distance between the centres of the Earth and the Sun, and $M_{S}$ is the mass of the Sun. Two stars orbit around their common centre of mass in circular orbits with period $n T$ , where $T$ is the period of Earth's revolution around the Sun.

The value of $n$ is _____.

Answer:

9.00

Solution:

$T = \frac{2 π R^{3 / 2}}{\sqrt{G M_{S}}}$

For binary stars,

$T' = \frac{2 π r^{3 / 2}}{\sqrt{G (M_{1} + M_{2})}}$

Put $M_{1} = 3 M_{S}$ , $M_{2} = 6 M_{S}$ and $r = 9 R$

$T' = \frac{2 π \times 9^{3 / 2} \times R^{3 / 2}}{\sqrt{G (3 M_{S} + 6 M_{S})}} = \frac{2 π \times 9^{3 / 2} \times R^{3 / 2}}{9^{1 / 2} \sqrt{G M_{S}}} = 9 (\frac{2 π R^{3 / 2}}{\sqrt{G M_{S}}})$

$∴ T' = 9 T$

Value of $n = 9$ .

Stream:JEE_ADVSubject:PhysicsTopic:GravitationSubtopic:Satellite Motion

⏱ 2mℹ️ Source: PYQ_2021

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