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 total machanical energy of the system is

Options

A. `-(1375)/(64)xx10^(35)J`
B. `-(1375)/(64)xx10^(38)J`
C. `-(1375)/(64)xx10^(34)J`
D. `-(1375)/(64)xx10^(37)J`

Answer

B

Explanation

Total machanical energy `=K.E+P.E`
`=2((1)/(2)mv^(2))-(2GMm)/(r)-(Gm^(2))/(2r)=m[(G(4M+m))/(4r)-(2GM)/(r)-(Gm)/(2)]=-(Gm)/(r)[M+(m)/(4)]`
`=-((20)/(3)xx10^(-11))((11)/(8)xx10^(30))xx(1)/(10^(11))(2xx10^(30)+(11)/(32)xx10^(30))=-(1375)/(64)xx10^(38)J`