A machine gun fires a bullet of mass $40\,g$ with a velocity $1200\,\,m{s^{ - 1}}.$ The man holding it can exert a maximum force of $144\,N$ on the gun. How many bullets can he fire per second at the most
A machine gun fires a bullet of mass $40\,g$ with a velocity $1200\,\,m{s^{ - 1}}.$ The man holding it can exert a maximum force of $144\,N$ on the gun. How many bullets can he fire per second at the most
$1$
$4$
$2$
$3$
A machine gun fires a bullet of mass $40\,g$ with a velocity $1200\,\,m{s^{ - 1}}.$ The man holding it can exert a maximum force of $144\,N$ on the gun. How many bullets can he fire per second at the most
$u = $ velocity of bullet
$\frac{{dm}}{{dt}} = $Mass fired per second by the gun
$\frac{{dm}}{{dt}}$= Mass of bullet $(mB) ×$ Bullets fired per sec $(N)$
Maximum force that man can exert $F = u\;\left( {\frac{{dm}}{{dt}}} \right)$
$\therefore F = u \times {m_B} \times N$
$⇒ N = \frac{F}{{{m_B} \times u}} = \frac{{144}}{{40 \times {{10}^{ - 3}} \times 1200}} = 3$
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