Question

A machine gun fires a bullet of mass 40g with a velocity 1200m/s. The man holding it can exert a maximum force of 144N on the gun. How many bullets can be fired per second at the most?
A. Only one
B. three
C. any number of bullets
D. 144$\times$48

Answer 1

In this problem, we have to use the application of Newton’s third law of motion
From Newton’s an important conclusion comes out that forces always occur in pairs.

Complete step by step answer:
Given mass, m=40g =0.04 kg
velocity of bullet, v= 1200m/s
The man holding it can exert a maximum force of 144N on the gun.
It means the man is exerting this much force on the gun. So as per Newton’s third law, an equal and opposite force must be exerted by the machine gun on the man.
Also, momentum is given by p=mv
Since a large number of bullets are coming out so the force can be written in terms of change in momentum,
F=nmv
This must be equal to 144N
144=n$\times$0.04$\times$1200
n= 3
Hence the machine gun should fire 3 bullets per second to get hold up by the man.

So, the correct answer is “Option B”.

Note:
A single force can never exist and this is a universal law applicable everywhere. That’s why it is also called the action-reaction law of Newton’s and it is very common.
This explains Newton’s third law and how Newton's third law can be written in terms of change in the momentum of a body.