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Conservation of Momentum

A gun weighin...

Question

A gun weighing 4 kg fires a bullet of 40 g with a velocity of $500 m s^{-} 1$ . With what velocity does the gun recoil?

A

$5 m s^{-} 1$

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B

$10 m s^{-} 1$

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C

$20 m s^{-} 1$

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D

$4 m s^{-} 1$

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Solution

The correct option is A
$5 m s^{-} 1$

Mass of gun $m_{1}$ = 4 kg,
Mass of bullet $m_{2}$ = 40 g = 0.04 kg
Let velocity of bullet be $v_{2}$
$V_{2}$ = $500 m s^{-} 1$
Using conservation of momentum : m1v1 = m2v2
Recoil velocity $v_{1} = \frac{m_{2} v_{2}}{m_{1}}$
$= \frac{0.04 \times 500}{4} = 5 \frac{m}{s}$

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