JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Gravitation

Consider a binary star system of star A and star B with masses

m_{A}

and

m_{B}

revolving in a circular orbit of radii

r_{A}

and

r_{B}

, respectively. If

T_{A}

and

T_{B}

are the time period of star A and star B, respectively, then :

(A) $T_{A} = T_{B}$ ✓ Correct
(B) $T_{A} > T_{B}$ (if $m_{A} > m_{B}$ )
(C) $\frac{T _{A}}{T _{B}} = (\frac{r _{A}}{r _{B}})^{\frac{3}{2}}$
(D) $T_{A} > T_{B}$ (if $r_{A} > r_{B}$ )

Answer: (A)

Solution

Both stars move about their common centre of mass, which lies on the line joining them, and that line stays straight as the system turns. The two stars therefore sweep equal angles in equal times and share a single angular velocity

ω

, whatever their masses or orbital radii. Since

T = \frac{2 π}{ω}

, the two periods are equal,

T_{A} = T_{B}

JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Single correct option

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