Questions

Binary stars of comparable masses rotate under the influence of each other's gravity at a distance ${[2 G / ω^{2}]}^{1 / 3}$ where $ω$ is the angular velocity of each of the system. If difference between the masses of two stars is 6 units. Find the ratio of the masses of smaller to bigger star.

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4:10

1:7

2:8

3:9

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detailed solution

Correct option is B

m1r1=m2r2 or r1=m2rm1+m2 (i)m1r1ω2=Gm1m2r2⇒ω2=Gm1+m2r3[From (i)] or r=Gm1+m2ω21/3m1+m21/3=2m1+m2=8and m2−m1=6 (given) which gives m1=1 and m2=7 units m1m2=17

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