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Centripetal Force

A double star...

Question

A double star system consists of two stars $A$ and $B$ which have time periods $T_{A}$ and $T_{B},$ radius $R_{A}$ and $R_{B}$ and the mass $M_{A}$ and $M_{B}$ respectively. Then

T_{A} > T_{B}^{'}

then

R_{A} > R_{B}

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T_{A} > T_{B}^{'}

then

M_{A} > M_{B}

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{(\frac{T_{A}}{T_{B}})}^{2} = {(\frac{R_{A}}{R_{B}})}^{3}

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T_{A} = T_{B}

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Solution

The correct option is D $T_{A} = T_{B}$
In double star system, they both move with the same angular velocity about the common centre of mass of the system, due to their mutual gravitational attraction.

$ω_{A} = \frac{2 π}{T_{A}}; ω_{B} = \frac{2 π}{T_{B}}$

$∴ ω_{A} = ω_{B}$

$\Rightarrow \frac{2 π}{T_{A}} = \frac{2 π}{T_{B}}$

$\Rightarrow T_{A} = T_{B}$

 Hence, $(D)$ is the correct answer.

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