Question

Three balls $A,B$ and $C$ are placed on a smooth horizontal surface. Given that $m_A=m_C=4m_B$. Ball $B$ collides with ball $C$ with an initial velocity $v$ as shown in figure. Find the total number of collisions between the balls. All collisions are elastic.

Answer 1

When ball B moves towards C ball, so first, collision is between B ball & C ball.

After collision $vB$ and $vC$ is speed of balls B & C.

$v_B=(mB-mCmB+mC)v$

$v_C=(2mBmB+mC)v$ $(mC=4mB)$ i.e. $mC>4mB$

From the above equations we can say that $mC$ has negative sign, so after this collision ball B will move in opposite direction towards ball A.

$\therefore$ Ball B makes another collision with A.

So, number of collisions made by ball B is two.