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Q.

Two identical spherical stars each having a mass equal to that of the sun move in a common circular orbit of radius equal to the earth's orbital radius, under their mutualgravitational interaction. Their time period of rotation equals

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a

2yr

b

1yr

c

22yr

d

2yr

answer is A.

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Detailed Solution

Mv2R=GM24R2 v2=GM4R Time period,T=2πRV=2πRGM/4R =2πGM×2×R3/2  If M=Msun ,R=Rearth - sun,  Kepler's 3rd  law gives us,  Tearth =2πGMsun ×Rearth-sun 3/2=1yr.∴T=2πGMsun ×2×Rearth-sun 3/2=2×1yr=2yr.
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Two identical spherical stars each having a mass equal to that of the sun move in a common circular orbit of radius equal to the earth's orbital radius, under their mutualgravitational interaction. Their time period of rotation equals