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4-1.Newton's Laws of Motion
easy
A shell of mass $0.020\; kg$ is fired by a gun of mass $100\; kg$. If the muzzle speed of the shell is $80 \;m s^{-1}$, what is the recoil speed in $m/s$ of the gun ?
A
$0.8$
B
$0.08$
C
$0.016$
D
$0.16$
Solution
Mass of the gun, $M=100 \,kg$
Mass of the shell, $m=0.020 \,kg$
Muzzle speed of the shell, $v=80 \,m / s$
Recoil speed of the gun $=V$
Both the gun and the shell are at rest initially.
Initial momentum of the system $=0$
Final momentum of the system $=m v-M V$
Here, the negative sign appears because the directions of the shell and the gun are opposite to each other.
According to the law of conservation of momentum:
Final momentum $=$ Initial momentum
$m v-M V=0$
$\therefore V=\frac{m v}{M}$
$=\frac{0.020 \times 80}{100 \times 1000}=0.016 \,m / s$
Standard 11
Physics
