From a rifle of mass $5\ kg$, a bullet of mass $50\ gram$ is fired with an initial velocity of $50\ m/s$. Calculate the initial recoil velocity of the rifle.

Here, mass of the bullet $m=50\ gm=\frac{50\ gm}{1000}=0.05\ kg.$

Initial velocity of the bullet $u=50\ m/s$

Mass of the rifle $M=5\ kg.$

Final velocity of the bullet $v=0$

Final velocity of the rifle $V=0$

Let initial recoil velocity of the rifle is $U$.

Therefore, according to the law of conservation of momentum

$mu+MU=mv+MV$

Or $0.05\times50+5\times U=0.05\times0+5\times0$

Or $0.25+5U=0$

Or $5U=-0.25$

Or $U=-\frac{0.25}{5}$

Or $U=-0.5\ m/s$   [$-ve$ sign indicates the opposite direction]

Thus, the initial recoil velocity of the riffle is $-0.5\ m/s$.

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Updated on: 10-Oct-2022

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