Q.

A double star is a system of two stars moving around the centre of mass of the system due to gravitation. The distance between the components of the double star is d=GMT2xπ21/y (given, the total mass is M and time period is T). Find the value x+y

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answer is 7.

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Detailed Solution

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r1=m2dm1+m2&Gm1m2d2=m1r1ω2

Gm1m2d2=m1m2dm1+m24π2T2

Gm1+m2d3=4π2T2 Given M=m1+m2

GMd3=4π2T2d=GMT24π21/3

compairing d=GMT2xπ21/y=GMT24π21/3 x=4 and y=3

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