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Q. 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

AIPMTAIPMT 2015Work, Energy and Power

Solution:

Total initial energy of two particles
$=\frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2$
Total final energy of two particles
$=\frac{1}{2}m_2v_2^2+\frac{1}{2}m_1v_1^2+ \varepsilon $
Using energy conservation principle,
$\frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2 =\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2 +\varepsilon $
$\therefore \frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2 -\varepsilon =\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2$