First slide

The steps in collision

Question

When a body of mass m₁ moving with uniform velocity $40 {ms}^{- 1}$ collides with another body of mass m₂ at rest, then the two together begin to move with uniform velocity of $30 {ms}^{- 1}$ . The ratio of the masses (i. e. m₁/m₂ ) of the two bodies will be

Easy

A

1 : 3
B

3: 1
C

1 : 1.33
D

1 : 0.75

Solution

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

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