Work Energy and Power - Result Question 60
63. A stationary particle explodes into two particles of masses $m_1$ and $m_2$ which move in opposite directions with velocities $v_1$ and $v_2$. The ratio of their kinetic energies $E_1 / E_2$ is
(a) $m_1 v_2 / m_2 v_1$
(c) $m_1 / m_2$
(b) $m_2 / m_1$
(d) 1
[2003]
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Answer:
Correct Answer: 63. (b)
Solution:
- (b) From conservation law of momentum, before collision and after collision linear momentum (p) will be same. That is, initial momentum $=$ final momentum.
$\Rightarrow 0=m_1 v_1-m_2 v_2 \Rightarrow m_1 v_1=m_2 v_2$
$p_1=p_2$
Now, $E=\frac{p^{2}}{2 m}$
$\therefore \frac{E_1}{E_2}=\frac{p_1^{2}}{2 m_1} \times \frac{2 m_2}{P_2^{2}}$
$\Rightarrow \frac{E_1}{E_2}=\frac{m_2}{m_1}[p_1=p_2]$
