Question

A ''double star'' is a composite system of two stars rotating about their center of mass under their mutual gravitational attraction. Let us consider such a ''double star'' which has two stars of masses 'm' and '2m' at a separation '1'. If T is the time period of rotation about their enter of mass then.

• A. $T=2\pi\sqrt\frac{l^3}{mG}$
• B. $T=2\pi\sqrt\frac{l^3}{2mG}$
• C. $T=2\pi\sqrt\frac{l^3}{3mG}$
• D. $T=2\pi\sqrt\frac{l^3}{4mG}$

Answer 1

Answer: (C)

$T=2\pi\sqrt\frac{l^3}{3mG}$

Answer 2

consider origin at pratical of mass 2m, we have centre of mass is 1/3 and 21/3 from m. $\frac{2l}{3} \, \omega^2 = \frac{Gm(2m)}{l^2}$ then find T