# A man fires the bullet of mass m each with a velocity v from a machine gun. If he fires n bullets every second, the reactional force per second on the man will be

$(a)\;\frac{m}{v}n \quad (b)\;mnv \quad (c)\;\frac{mv}{n} \quad(d)\;\frac{vn}{m}$

Per Newton's second law, $F = \large\frac{dp}{dt}$
Total mass of bullet fired in 1 second$= m \times n$
$\Rightarrow$ Change in momentum per second $dp =p_2 - p_1 = mnv-0$
$\Rightarrow F = \large\frac{mnv - 0}{1}$$= mnv$
edited Aug 20, 2014