Question

Four balls $A,B,C$ and $D$ are placed on a smooth horizontal surface. Ball $B$ collides with ball $C$ first with an initial velocity $V.$ if all collisions are perfectly elastic then total number of collisions among balls are:-

• A. $10$
• B. $4$
• C. $3$
• D. Cannot be determined

Answer 1

The correct option is C $3$

Given:
Velocity of ball $B$ be $V.$


$Aftercollision\left(1^{st}collision\right):$

$V_B=\frac{m_1-m_2}{m_1+m_2}V$
$V_B=\frac{m-2m}{3m}V=-\frac{V}{3}$ (moving towards $A$ )

$V_C=\frac{2m_1}{m_1+m_2}v=\frac{2m}{3m}v=\frac{2}{3}v$ (moving towards $D$)



$2^{nd}collision:$

$C$ and $D$ have same mass, so $C$ comes to rest after colliding with $D$ and $D$ attains $\frac{2V}{3}$ velocity towards right.

$3^{rd}collision:$

Similarly, $B$ and $A$ have same masses, hence after collision $B$ comes to rest and $A$ attains $\frac{V}{3}$ velocity towards left.


Therefore the total number of collisions are $3$

Hence, option (c) is the correct answer.