Question

Two balls marked 1 and 2 are of the same mass 'm' and a third ball marked 3 s of mass 'M' are arranged over a smooth horizontal surface as shown in figure. Ball 1 moves with a velocity $v{­}_1$ towards balls 2 and 3. All the collisions are assumed to be elastic. If M >> m, then the total number of collisions between the balls will be
,

• A. One
• B. Two
• C. Three
• D. Four

Answer 1

The correct option is C Three

Collision 1: Between 1 and 2
Collision 2: Velocity of ball 2 after collision with ball 3 = $v_2=\left(\frac{m-M}{m+M}\right)v_1$, M > m $\therefore v_2$ < 0
The negative sign indicates that, after the second collision, ball 2 will move in opposite direction towards the ball 1 which is at rest after the first collision.
Collision 3: Ball 2 will make another collision with ball 1 and come to rest and ball 1 and ball 3 will continue moving in opposite directions with ball 2 at rest. Hence, in this case, there are three collisions in all between the balls.
Thus the correct choice is (c).