Find the recoil velocity of a gun having a mass equal to 5 kg, if a bullet of 25 g acquires the velocity of 500 m/s after firing from the gun.

2.5 m/s

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2.5 m/s

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10 m/s

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5 m/s

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Solution

The correct option is B
2.5 m/s

Here given,
Mass of bullet $(m_{1}) = 25 g = 0.025 k g$
Velocity of bullet before firing $(u_{1}) = 0$
Velocity of bullet after firing $(v_{1}) = 500 m / s$
Mass of gun $(m_{2}) = 5 k g$
Velocity of gun before firing, $(u_{2}) = 0$
Velocity of gun after firing = ?
We know that, $m_{1} u_{1} + m_{2} u_{2}$ $= m_{1} v_{1} + m_{2} v_{2}$
$0.025 k g \times 0 + 5 k g \times 0$ $= 0.025 k g \times 500 m / s + 5 k g \times v_{2}$
$0 = 12.5 k g m / s + 5 k g \times v_{2}$
$5 k g \times v_{2} = - 12.5 k g m / s$
$v_{2} = \frac{12.5 k g m / s}{5 k g} = 2.5 m / s$
Thus, recoil velocity of gun is equal to 2.5 m/s. Here negative (- ve) sign shows that gun moves in the opposite direction of bullet.

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