Question

A double star consists of two stars having masses M and 2 M. The distance between their centres is equal to r. They revolve under their mutual gravitational interaction. Then, which of the following statements is/are correct? 

(a) Heavier star revolves in orbit of radius 2r/3 

(b) Both of the stars revolve with the same period which is equal to 2π/√2GM/3 r^3/2

(c) Kinetic energy of heavier star is twice that of the other star 

(d) None of the above

Answer 1

The correct option is (b) Both of the stars revolve with the same period which is equal to 2π/√2GM/3 r^3/2.

Explanation:

The centre of mass of the double star system remains stationary and both the stars revolve round in circular orbits which are concentric with the centre of mass. 

The distance of centre of mass from the heavier star

= (Mr + 2M x 0) / (M + 2M) = r/3

Hence, the heavier star revolves in a circle of radius r/3 while the lighter star in a circle of radius 2r/3. So, option (a) is not correct.

So, KE of lighter star is two times that of heavier star' So, option (c) is wrong.