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Momentum

When a body o...

Question

When a body of mass $m_{1}$ moving with uniform velocity $40 m s^{- 1}$ collides with another body of mass $m_{2}$ at rest, then the two together begin to move with uniform velocity of $30 m s^{- 1}$ . The ratio of the mass (i.e., $\frac{m_{1}}{m_{2}}$ ) of the two bodies will be

1 : 3

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3 : 1

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1 : 1.33

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1 : 0.75

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Solution

The correct option is C $3 : 1$
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
$40 m_{1} = (m_{1} + m_{2}) 30$
$40 m_{1} - 30 m_{1} = 30 m_{2}$
$10 m_{1} = 30 m$
$\frac{m_{1}}{m_{2}} = \frac{3}{1}$ .

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