Question

A circular ring of mass M and radius R is placed in a gravity free space. A small particle of mass m is placed on the axis of ring at a distance $\sqrt{3}$R from the centre of the ring. If particle and ring are released from rest. Speed with which particle passes through the centre of the ring is

• A. $\sqrt{\frac{2GM}{R}}$
• B. $\sqrt{\frac{G{M}^2}{2mR}}$
• C. $\sqrt{\frac{G{M}^2}{(M+m)R}}$
• D. $\sqrt{\frac{G(M+m{)}^2}{2MR}}$

Answer 1

The correct option is C $\sqrt{\frac{G{M}^2}{(M+m)R}}$

By COE $\Rightarrow \frac{GMm}{2R}=\frac{1}{2}M{V}^2+\frac{1}{2}m{V}_0^2$ ----(1)
By COM $\Rightarrow MV=m{V}_0$ ----(2) solving (1) & (2)
$V_0=\sqrt{\frac{G{M}^2}{(M+m)R}}$