Question

Two particles of masses m₁, m₂ move with initial velocities u₁ and u₂. On collision, one of the particles get excited to higher level, after absorbing energy ε. If final velocities of particles be v₁ and v₂ then we must have
(a) $\frac{1}{2}m_{1}u_{1}^{2}+\frac{1}{2}m_{2}u_{2}^{2}=\frac{1}{2}m_{1}v_{1}^{2}+\frac{1}{2}m_{2}v_{2}^{2}-\epsilon$
(b) $\frac{1}{2}m_{1}u_{1}^{2}+\frac{1}{2}m_{2}u_{2}^{2}-\epsilon=\frac{1}{2}m_{1}v_{1}^{2}+\frac{1}{2}m_{2}v_{2}^{2}$
(c) $\frac{1}{2}m_{1}^{2}u_{1}^{2}+\frac{1}{2}m_{2}^{2}u_{2}^{2}+\epsilon=\frac{1}{2}m_{1}^{2}v_{1}^{2}+\frac{1}{2}m_{2}^{2}v_{2}^{2}$
(d) $m_{1}^{2}u_{1}+m_{2}^{2}u_{2}-\epsilon=m_{1}^{2}v_{1}+m_{2}^{2}v_{2}$

Answer 1

Answer: (b) because energy must be added to the right side of the equation

to conserve energy - the collision is inelastic since some of the initial KE is lost in the collision due to absorption of energy by one of the masses.