Q56 / 57 · JEE Advanced 2021 (Paper 2) · Physics

The distance between two stars of masses 3MS and 6MS is 9R. Here R is the mean distance between the centres of the Earth and the Sun, and MS is the mass of the Sun. Two stars orbit around their common centre of mass in circular orbits with period nT, whereT is the period of Earth's revolution around the Sun.

The value of n is _____.

Correct answer: 9

Solution

T=2πR3/2GMS

For binary stars,

T'=2πr3/2GM1+M2

Put M1=3MS,M2=6MS and r=9R

T'=2π×93/2×R3/2G3MS+6MS=2π×93/2×R3/291/2GMS=92πR3/2GMS

∴  T'=9T

Value of n=9.

Hence, the correct answer is 9.

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