Three balls and  are placed on a smooth horizontal surface. Ball  collides with ball  with an initial velocity  as shown in Fig. Find the total number of collisions between the balls (all collisions are elastic)

(2)

For the first collision,

   (i)

By momentum conservation

         (ii)

From Eqs. (i) and (ii), and

For the second collision,

(iii)

By momentum conservation,

Or

    (iv)

From Eqs. (iii) and (iv),

Clearly

Therefore, ‘ ’ cannot collide with ‘ ’ for the second time

Hence, the total number of collisions is 2