Q. A machine gun fires a bullet of mass 40 g with a velocity$\ 1200{ms}^{- 1}$. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can be fired per second at the most?

A) Only one
B) Three
C) Can fire any number of bullets
D) $144 \times 48$
Explanation

(b) From Newton’s second law
$F = n \bullet \left( \frac{\mathrm{\Delta}p}{\mathrm{\Delta}t} \right)$
Here, $F = Force,\ n = number\ of\ bullets\ fired\ per\ second.$
$\frac{\mathrm{\Delta}p}{\mathrm{\Delta}t} = rate\ of\ change\ of\ momentum\ of\ one\ bullet.$
$\Longrightarrow F = n\left\lbrack \frac{mv - 0}{\mathrm{\Delta}t} \right\rbrack$
$\Longrightarrow F = n \times \frac{mv}{\mathrm{\Delta}t}$
$Hence,\ \ F = 144\ N,m = 40g = 40 \times 10^{3}kg$
$and\ v = 1200\ {ms}^{- 1},\ \mathrm{\Delta}t = 1\ s.$
$\therefore 144 = n \times \frac{40 \times 10^{- 3} \times 1200}{1}$
$orn = \frac{144}{4 \times 12} \Longrightarrow n = 3$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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