Question

A particle of mass $m$ moving with a speed $v$ hits elastically another stationary particle of mass $2m$ in a fixed smooth horizontal circular tube of radius $r$. Find the time when the next collision will take place?

Answer 1

By momentum conservation.

$v_1=\frac{2m-m}{3m}v=\frac{v}{3}{v}_2=\frac{2m}{3m}v=\frac{2}{3}v$

after collision relatiive velocity $=v_1+v_2$

$=\frac{v}{3}+\frac{2v}{3}=v$

Now time taken to cover 2$\pi$ r distance is time of next collision.

$t=\frac{2\pi r}{v}$