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Q.

A double star is a system of two stars of masses m and 2m, rotating about their centre of mass only under their mutual gravitational attraction. If r is the separation between these two stars then their time period of rotation about their centre of mass will be proportional to

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a

m1/2

b

r

c

r3/2

d

m−1/2

answer is A, D.

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Detailed Solution

F=2Gm2r2

Fc=mrω2=2Gm2r2

ω=(2Gmr3)1/2

Time periodT=2πω

=2π(r32Gm)1/2

=2π2Gr3/2m−1/2

T∝r3/2,      T∝m−1/2

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