A bullet of mass $10$ g is fired from a gun of $1$ kg with recoil velocity of gun is $5 m / s$ . The muzzle velocity will be.

30 k m / m i n

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60 k m / m i n

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30 m / s

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500 m / s

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Solution

The correct option is D $500 m / s$
Conservation of linear momentum gives,

$m_{1} v_{1} + m_{2} v_{2} = 0$

$m_{1} v_{1} = - m_{2} v_{2}$

$v_{1} = \frac{- m_{2} v_{2}}{m_{1}}$

Given, $m_{1} = 10$ g $= (\frac{10}{1000})$ kg,

$m_{2} = 1$ kg,

$v_{2} = - 5 m / s$

$∴ v_{1} = \frac{+ 1 \times 5}{10 / 1000}$
or $v_{1} = 500 m / s$ .

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