Question

Three identical balls each of mass $m=0.5$ kg are connected with each other as shown in Figure and rest over a smooth horizontal table. At moment $t=0$, ball B is imparted a horizontal velocity $v_0=9m{s}^{-1}$. Calculate velocity of A just before it collides with ball C.

Answer 1

Let $v_1$ be the initial velocity of A and C just before collision, $v_2$ and $v_2$ be the velocity

of B just before the collision. v is the velocity of ball A at which it is imparted,

v= 9 m/s.

Initially conservation of momentum,

mv= $m{v}_1+m{v}_1+m{v}_2$

v= v-2$v_2$

$v_2=v-2v_1$------ (1)

From conservation of K.E,

$\frac{1}{2}m{v}^2=\frac{1}{2}m{v}_1^2+\frac{1}{2}m{v}_1^2+\frac{1}{2}m{v}_2^2$

$v^2=2v_1^2+v_2^2$----- (2)

(1) in (2)-

$v^2=2v_1^2+v^2-4v{v}_1+4v_1^2$

6$v_1^2$= 4v$v_1$

$v_1=v\left(\frac{2}{3}\right)v_1=9\left(\frac{2}{3}\right)=6m/s$