Q108 / 200 · NEET 2003 · Physics

A stationary particle explodes into two particles of masses $m_1$ and $m_2$ which more in opposite direction with velocities $v_1$ and $v_2$. The ratio of their kinetic energies $E_1 / E_2$ is:

  • Correct answer
    A
    $m_2 / m_1$
  • B
    $m_1 / m_2$
  • C
    1
  • D
    $m_1 m_2 / m_2 m_1$

Solution

According to law of conservation of linear momentum $$ \begin{aligned} & m_1 v_1=m_2 v_2 \quad \ldots \text { (i) } \\ & E_1=\frac{1}{2} m_1 v_1^2, E_2=\frac{1}{2} m_2 v_2^2 \\ & \therefore \frac{E_1}{E_2}=\frac{\frac{1}{2} m_1 v_1^2}{\frac{1}{2} m_2 v_1^2}=\frac{\left(m_1 v_1\right)^2}{\left(m_2 v_2\right)^2} \times \frac{m_2}{m_1} \\ & \therefore \frac{E_1}{E_2}=\frac{m_2}{m_1} \end{aligned} $$

Hence, the correct answer is option: 'A'.

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