First slide

Collisions

Question

A body of mass m₁ moving with a velocity 3 ms^–1 collides with another body at rest of mass m₂. After collision the velocities of the two bodies are 2 ms^–1 and 5ms^–1 respectively along the direction of motion of m₁. The ratio m₁ / m₂ is

Moderate

A

$\frac{5}{12}$
B

$5$
C

$\frac{1}{5}$
D

$\frac{12}{5}$

Solution

If target is at rest then final velocity of bodies are
$v_{1} = (\frac{m_{1} - m_{2}}{m_{1} + m_{2}}) u_{1}$ …(i) and $v_{2} = \frac{2 m_{1} u_{1}}{m_{1} + m_{2}}$ …(ii)
From (i) and (ii) $\frac{v_{1}}{v_{2}} = \frac{m_{1} - m_{2}}{2 m_{1}} = \frac{2}{5} \Rightarrow \frac{m_{1}}{m_{2}} = 5$

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