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AIIMS 201827 May
Exam
AIIMS
Year
2018
Date
27 May
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

AIIMS 2018 · 27 May · Physics · Center of Mass, Momentum and Collision

A body of mass m_1 collides elastically with another body of mass...

A body of mass m1m_1 collides elastically with another body of mass m2m_2 at rest. If the velocity of m1m_1 after collision becomes 2/32 / 3 times its initial velocity, the ratio of their masses is

Options

  1. A1:51: 5
  2. B5:15: 1
  3. C5:25: 2
  4. D2:52: 5

Correct answer

B. 5:15: 1

Step-by-step solution

Let vv be the initial velocity of body of mass m1m_1 before collision. Since collision is elastic both momentum and kinetic energy are conserved. ∴m1v=m123v+m2v2orm1(v−23v)=m2v2\therefore m_1 v=m_1 \frac{2}{3} v+m_2 v_2 or m_1\left(v-\frac{2}{3} v\right)=m_2 v_2 Also, 12m1v2=12m1(23)2v2+12m2v22\frac{1}{2} m_1 v^2=\frac{1}{2} m_1\left(\frac{2}{3}\right)^2 v^2+\frac{1}{2} m_2 v_2^2 or m1(v2−49v2)=m2v22orm1m2=9v225v2m_1\left(v^2-\frac{4}{9} v^2\right)=m_2 v_2^2 or \frac{m_1}{m_2}=\frac{9 v_2^2}{5 v^2} Equating (i) and (ii), we get 9v225v2=3v2v or  v2v=53∴m1m2=3×53=51\begin{aligned} & \frac{9 v_2^2}{5 v^2}=\frac{3 v_2}{v} \text{\text{ or } } \frac{v_2}{v}=\frac{5}{3} \\ & \therefore \frac{m_1}{m_2}=\frac{3 \times 5}{3}=\frac{5}{1}\end{aligned}
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