A particle of mass $m_1$ is moving with a velocity $v_1$ and another particle of mass $m_2$ is moving with a…

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:
  1. $E_1 < E_2$
  2. $\frac{E_1}{E_2}=\frac{m_1}{m_1}$
  3. $E_1 > E_2$
  4. $E_1=E_2$

Solution

We know that K.E. $=\frac{P^2}{2 m}$ $\begin{array}{ll} \therefore & \frac{E_1}{E_2}=\frac{P_1^2 / 2 m_1}{P_2^2 / 2 m_2} \\ \Rightarrow \quad \frac{E_1}{E_2}=\frac{m_2}{m_1} \end{array}$ Here $\quad m_1=m_2$ $\therefore \quad E_1 < E_2$ .

Asked in: NEET 2004

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