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  4. A particle of mass m1 is moving with a velocity v1 and another particle of mass m2 is moving with a velocity v2 Both of them have the same momentum but their different kinetic energies are E1 and E2 respectively. If m1 > m2 , then

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Q. A particle of mass $m_1$ is moving with a velocity $v_1$ and another particle of mass $m_2$ is moving with a velocity $v_2$ Both of them have the same momentum but their different kinetic energies are $ E_1$ and $E_2$ respectively. If $ m_1 > m_2 $, then

MP PMTMP PMT 2007Work, Energy and Power

Solution:

Kinetic energy $=\frac{p^{2}}{2 m}$
$\therefore \frac{E_{1}}{E_{2}}=\frac{p_{1}^{2} / 2 m_{1}}{p_{2}^{2} / 2 m_{2}}$
$ \Rightarrow \frac{E_{1}}{E_{2}}=\frac{m_{2}}{m_{1}} \text { as } m_{1}>m_{2}$
$\therefore E_{1}< E_{2}$