First slide

Special cases

Question

Two balls A and B of same mass and a third ball of mass M are arranged over a smooth horizontal surface as shown in fig.(1) Ball A moves with a velocity v₁
towards ball B and C. All collisions are assumed to be elastic. lf. m>M , the number of collisions between B and C

Moderate

A

1
B

2
C

3
D

4

Solution

The first collision will be between balls, A and B. In this collision ball A will come to rest while ball B will move forward with velocity $v_{1}$ . This ball B will strike ball C (at rest). Let v₂ and v₃ be the speeds of ball B and ball C respectively after collision. We have
$v_{2} = (\frac{m - M}{m + M}) v_{1} and v_{3} = (\frac{2 m}{m + M}) v_{1} when M < m, V_{2} < V_{3} and both have same direction . Now ball B cannot collide with ball C because velocity v_{2} of ball B is less tha n the velocity v_{3} of ball C . So, there will be only one collision$

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