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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 absorbing energy \( \varepsilon \) if final velocities of particles be \( v_{1} \) and \( v_{2} \) then we must have
(a) \( \frac{1}{2} m_{1} u_{1}^{2}+\frac{1}{2} m_{2} u_{2}^{2}=\frac{1}{2} m_{1} v_{1}^{2}+\frac{1}{2} m_{2} v_{2}^{2}-\varepsilon \)
(b) \( \frac{1}{2} m_{1} u_{1}^{2}+\frac{1}{2} m_{2} u_{2}^{2}-\varepsilon=\frac{1}{2} m_{1} v_{1}^{2}+\frac{1}{2} m_{2} v_{2}^{2} \)
(c) \( \frac{1}{2} m_{1}^{2} u_{1}^{2}+\frac{1}{2} m_{2}^{2} u_{2}^{2}+\varepsilon=\frac{1}{2} m_{1}^{2} v_{1}^{2}+\frac{1}{2} m_{2}^{2} v_{2}^{2} \)
(d) \( m_{1}^{2} u_{1}+m_{2}^{2} u_{2}-\varepsilon=\frac{1}{2} m_{1}^{2} v_{1}^{2}+\frac{1}{2} m_{2}^{2} v_{2}^{2} \)
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