Question

A machine gun fires bullets of $50gm$ at the speed of $1000m/sec$. If an average force of $200N$ is exerted on the gun, the maximum number of bullets fired per minute is

Answer 1

Step 1: Given data.

As per the given data,

The mass of the bullets fired by the machine gun; $m=0.05kg$

The speed is given as:$v=1000m/s$

Average force;$F=200N$

Time is given as;$t=1s$

The time for which the maximum number of bullets fired has been asked as:$t=1\mathrm{minute}$

Step 2: Formula applied:

Force on the man is equal to the change in momentum of the bullets coming out of the gun

$F=\frac{mvn}{t}$

Where,

$F=$Average force

$m=$The mass of the bullets fired by the machine gun

$\mathrm{v}=$Speed or velocity

$t=$Time given

$\mathrm{n}=$the number of bullets fired per second

Step 3: Finding the number of bullets per second.

$$\begin{gathered} 200=\frac{0.05\times 1000\times n}{1} \\ 200=50\times n \\ \Rightarrow n=4 \end{gathered}$$

$\Rightarrow 4$bullets per second

$\Rightarrow$In one-minute $4x60=240$bullets.

Thus, the number of bullets fired in one minute is $240$.