c
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

\(m v-M V=0\)

\(\therefore V=\frac{m v}{M}\)

\(=\frac{0.020 \times 80}{100 \times 1000}=0.016 \,m / s\)