Question

A machine gun of mass 12 kg fires 25 g bullets at the rate of 4 bullets per second with a velocity of 500 ms^-1. What force must be applied to the gun to hold it in position?

• A. 20 N
• B. 12.5 N
• C. 50 N
• D. 75 N

Answer 1

The correct option is C

50 N

Step 1: Given data

Mass of the bullet $m=25g$

The velocity of the bullet $v=500m{s}^{-1}$

Step 2: Finding change in momentum of one bullet

Momentum $p=mv$

$p=\frac{25}{1000}\times 500$ [Since, $1g=\frac{1}{1000}kg$]

$p=12.5kgm{s}^{-1}$

Initially, bullet is at rest. So, the initial velocity is zero. So, the initial momentum is also zero.

Change in momentum$=12.5-0$

$=12.5kg-m{s}^{-1}$

Step 3: Finding change in momentum $\Delta p$ of 4 bullet

$\Delta p=4\times 12.5$

$=50kgm{s}^{-1}$

Force is the rate of change of momentum i.e. change in momentum per second. So, the force applied to hold the gun is equal to the magnitude of change in the momentum of the bullets in one second.

So, force applied to the gun$=50N$

Thus, option (c) is correct.