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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

if `T_(A)gtT_(B)` then `R_(A)gtR_(B)`

B

if `T_(A)gtT_(B)` then `M_(A)gtM_(B)`

C

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

D

`T_(A)=T_(B)`

Text Solution

Verified by Experts

The correct Answer is:
D

Figure shows a binary star system:
The gravitaional force of attraction between the stars will provide the necessary centripetal forces. In this case angular velocity of both stars is the same. Therefore time period remains the same.
`(omega=(2pi)/(T))`
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