Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is
A
2π√d33Gm
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B
12π√3Gmd3
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C
12π√d33Gm
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D
2π√3Gmd3
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Solution
The correct option is A2π√d33Gm
This is a double star system in which both the stars revolve around the centre of mass of the system with the same angular frequency ω(say).
On planet of mass m :
Fgravitation=Fcentripetal
⇒G(m)(2m)d2=mω2×2d3
[ Distance of COM of the system from the star of mass m=2d3]