Two particles of masses m_1, m_2 move with initial velocities u_1 and u_2. On collision, one of the particles get excited to higher level, after…

Two particles of masses $\displaystyle \mathrm{m}_1, \mathrm{~m}_2$ move with initial velocities $\displaystyle \mathrm{u}_1$ and $\displaystyle \mathrm{u}_2$. On collision, one of the particles get excited to higher level, after absorbing energy $\displaystyle \varepsilon$. If final velocities of particles be $\displaystyle v_1$ and $\displaystyle v_2$ then we must have :