In the previous question, if the collision is inelastic with, $e=\frac{2}{5}$, then repeat the above questions.

Let the velocities of two balls after the collision are $v_{A}and{v}_B$ respectively.
$$\begin{gathered} m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2 \\ \left[\because m_1=m_2=m,u_1=3m{s}^{-1},u_2=-7m{s}^{-1},v_1=v_A,v_2=v_B\right] \\ \Rightarrow m\times 3-m\times 7=m{v}_A+m{v}_B \\ \Rightarrow v_A+v_B=-4\dots \dots .\left(1\right) \end{gathered}$$

Now, we have, $e=\frac{2}{5},$ then
$e=\frac{2}{5}=\frac{v_A-v_B}{10}$
$\Rightarrow v_A-v_B=4......\left(2\right)$

Solving the equations (1) and (2), we get

$v_A=0{\mathrm{ms}}^{-1}and{v}_B=-4{\mathrm{ms}}^{-1}$

Hence, the velocity of the two balls are $v_A=0{\mathrm{ms}}^{-1}$ and $v_B=-4{\mathrm{ms}}^{-1}.$