Question

A double star is a system of two stars rotating about their centre of mass only under their mutual gravitational attraction. Let the stars have masses m and 2m and let their separation be l. Their time period of rotation about their centre of mass will be proportional to 

(a) l^3/2 

(b) l 

(c) m^1/2 

(d) m^-1/2

Answer 1

Correct Answer is: (a) l^3/2 ,(d) m^-1/2

F = G m(2m) / l² = mω²(2l / 3)

or 3mG / l3 = ω².

T = 2π / ω =2π √(l³ / 3mg).