Question
Two bodies undergo one$-$dimensional, inelastic, head$-$on collision. State an expression for the loss in the kinetic energy.

Answer

$\Delta K . E .=\frac{1}{2}\left(\frac{ m _1 m_2}{m_1+ m _2}\right)\left( u _1- u _2\right)^2\left(1- e ^2\right)$
Where, $\frac{m_1 m_2}{\left(m_1+m_2\right)}=\mu=$ reduced mass of the system.
$ii.$ As $e < 1, (1 – e^2)$ is always positive. Thus, there is always a loss of kinetic energy in an inelastic collision.

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