A triple star ststem consists of two stars each of mass m in the same circular orbit about central star with mass `M=2xx10^(33)kg`. The two outer stars always lie at opposite ends of a diameter of their common circular orbit the radius of the circular orbit is `r=10^(11)` m and the orbital period each star is `1.6xx10^(7)s` [take `pi^(2)=10` and `G=(20)/(3)xx10^(-11)Mn^(2)kg^(-2)`]
Q. The orbital velocity of each star is

Options

A. `(5)/(4)sqrt(10)xx10//s`
B. `(5)/(4)sqrt(10)xx10^(5)m//s`
C. `(5)/(4)sqrt(10)xx10^(2)m//s`
D. `(5)/(4)sqrt(10)xx10^(4)m//s`

Answer

D

Explanation

`T=(2pir)/(v)impliesv=(2pir)/(T)=((2)(sqrt(10))(10^(11)))/(1.6xx10^(7))=(5)/(4)sqrt(10)xx10^(4)m//s`