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

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Detailed Solution

After collision with B + C

$v_{B} {}^{'}= (\frac{m - 4 m}{m + 4 m}) v = - \frac{3}{5} v$

$v_{C}^{'} = (\frac{2 \times m}{m + 4 m}) v = \frac{2}{5} v$

After second collision between B + A

Now, Since final velocity of B < final velocity of C.

So, there will not be any further collisions.

Total number of collisions = 2

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