Work Energy and Power - Result Question 60

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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

======= ####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

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/work-energy-and-power/work-energy-and-power—result-question-60.md (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:

  1. (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, $E=\frac{p^{2}}{2 m}$

$\therefore \frac{E_1}{E_2}=\frac{p_1^{2}}{2 m_1} \times \frac{2 m_2}{P_2^{2}}$

$\Rightarrow \frac{E_1}{E_2}=\frac{m_2}{m_1}[p_1=p_2]$