question_answer

A bullet of mass 100 g is fired from a gun of mass 20 kg with a velocity of \[\text{1}00\,\text{m}{{\text{s}}^{-\text{1}}}.\]Then find the velocity of recoil of the gun.

Answer:

mass of bullet, \[m=100g=\frac{100}{1000}kg=\frac{1}{10}kg\] Velocity of bullet, \[v=100m{{s}^{-1}}\] Mass of gun, M = 20 kg Let recoil velocity of gun = V Before firing, the system (gun + bullet) is at rest; therefore, initial momentum of the system = 0 Final momentum of the system = momentum of bullet + momentum of gun \[\Rightarrow mv+MV=\frac{1}{10}\times 100+20V\] Applying law of conservation of momentum Final momentum = Initial momentum i.e. \[10+20V=0\] \[20V=-10\] or \[V=-\frac{10}{20}=-0.5\,\,m{{s}^{-1}}\] Negative sign shows that the direction of recoil velocity of the gun is opposite to the direction of the velocity of the bullet.