Two massive particles of masses M & m (M > m) are separated by a distance $\ell$. They rotate with equal angular velocity under their gravitational attraction. The linear speed of the particle of mass m is
Answer & explanation
Correct answer: option 2
The system rotates about the centre of mass. The gravitational force acting on the particle m accelerates it towards the centre of the circular path, which has the radius
$R=\frac{M \ell}{M+m}$
$\Rightarrow F=\frac{mv^2}{r} \Rightarrow \frac{GMm}{\ell^2}=\frac{mv^2}{\frac{M \ell}{M+m}}$
$\Rightarrow v=\sqrt{\frac{GM^2}{(M+m) \ell}}$