Question

Three particles each of mass $m$, can slide on fixed frictionless circular tracks in the same horizontal plane as shown. Particle $A$ moves with velocity $v_0$ and hits particle $B$ elastically. Assuming that $B$ and $C$ are initially at rest and lie along a radial line and the spring is initially relaxed before impact, find the velocity of $B$ after impact.

Answer 1

After collision of A with B. A-get rest and B move with tengential velocity v.

After some time B and C moved with constant or same angular speed.

By angular momentum conservation,

$\Rightarrow I_B{w}_0=I_{c}w+I_{B}w$

$\Rightarrow m{\left(2\pi \right)}^2\left(\frac{v_0}{2R}\right)=m{R}^{2}w+m{\left(2R\right)}^{2}w$

$\Rightarrow 2R{v}_0=w{R}^2\left(5\right)$

$\Rightarrow w=\frac{2}{5}\frac{v_0}{R}$

Speed of B after impact $=wR$

$=\frac{2}{5}{v}_0$

Hence, the answer is $\frac{2}{5}{v}_0.$