First slide

Collisions

Question

A body of mass m₁ moving with uniform velocity of 40 m/s collides with another mass m₂ at rest and then the two together begin to move with uniform velocity of 30 m/s. The ratio of their masses $\frac{m_{1}}{m_{2}}$ is

Moderate

A

0.75
B

1.33
C

3.0
D

4.0

Solution

Initial momentum of the system = $m_{1} \times 40 + m_{2} \times 0$
Final momentum of the system = $(m_{1} + m_{2}) \times 30$
By the law of conservation of momentum
$m_{1} \times 40 + m_{2} \times 0 = (m_{1} + m_{2}) \times 30$
$\Rightarrow 40 m_{1} = 30 m_{1} + 30 m_{2} \Rightarrow 10 m_{1} = 30 m_{2} = \frac{m_{1}}{m_{2}} = 3$

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