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A system of binary stars of mass m(A) an...

A system of binary stars of mass `m_(A)` and `m_(B)` are moving in circular orbits of radii `r_(A)` and `r_(B)` respectively. If `T_(A)` and `T_(B)` are at the time periods of masses `m_(A)` and `m_(B)` respectively then

A

`(T_(A))/(T_(B))=((r_(A))/(r_(B)))^(3//2)`

B

`T_(A)gtT_(B)("if "r_(A)gtr_(B))`

C

`T_(A)gtT_(B)("if "m_(A)gtm_(B))`

D

`T_(A)=T_(B)`

Text Solution

Verified by Experts

The correct Answer is:
D
`(Gm_(A)m_(B))/((r_(A)+r_(B))^(2))=(m_(A)r_(A)4pi^(2))/(T_(A)^(2))=(m_(B)r_(B)4pi^(2))/(T_(B)^(2))`
`implies m_(A)r_(A)=m_(B)r_(B)`
`therefore T_(A)=T_(B)`

Aliter : The gravitational force of attraction between the stars will provide the necessary centripetal force. In this case angular velocity of both stars is the same. Hence `T_(A)=T_(B)`.
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