If an ivory ball of mass 2m moving with a velocity 'v' strikes head on to a close row of three identical ivory balls each of mass m as shown in the figure. Then after the collisions which may be assumed as elastic, which of the following would occur   

${\text{u}}_1=\text{v}\text{for}{\text{m}}_1$

${\text{u}}_2=\text{0}\text{for}{\text{m}}_2$

$v_1=\frac{\left({\text{m}}_{\text{1}}-{\text{m}}_{\text{2}}\right){\text{u}}_{\text{1}}}{\left({\text{m}}_{\text{1}}+{\text{m}}_{\text{2}}\right)}+\frac{{\text{2m}}_{\text{2}}{\text{u}}_{\text{2}}}{\left({\text{m}}_{\text{1}}+{\text{m}}_{\text{2}}\right)}$

$=\frac{\text{m}\times \text{v}}{3\text{m}}+0$

${\text{v}}_{\text{1}}=\frac{\text{v}}{\text{3}}$

${\text{v}}_{\text{2}}=\frac{{\text{2m}}_{\text{1}}{\text{u}}_{\text{1}}}{\left({\text{m}}_{\text{1}}+{\text{m}}_{\text{2}}\right)}+\frac{\left({\text{m}}_{\text{2}}-{\text{m}}_{\text{1}}\right){\text{u}}_2}{\left({\text{m}}_{\text{1}}+{\text{m}}_{\text{2}}\right)}$

$=\frac{2{\text{m}}_{\text{1}}\text{v}}{3\text{m}}$

$=\frac{\text{4mv}}{\text{3m}}$

${\text{v}}_{\text{2}}\Rightarrow \frac{4}{3}\text{v}$

For ${\text{2}}^{\text{nd}}\text{case}$                             

V for${\text{2}}^{\text{nd}}$  body = u for${\text{1}}^{\text{st}}$  body$=\frac{4}{3}\text{v}$

V for $3^{\text{rd}}$ body $=\frac{4}{3}\text{v}$

So the ball numbered 3 moves with velocity $\frac{4}{3}\text{v}$ and number 4 moves with $\frac{\text{v}}{\text{3}}$

$\Rightarrow$ The ball numbered 3 moves with velocity $\frac{\text{'}4\text{v'}}{3}$ and the striking ball

moves with velocity$\frac{\text{'v'}}{\text{3}}$