A machine gun fires a bullet of mass $m$ with a speed of $v m / s$ . The person holding the gun can exert a maximum force $F$ on it. What is the number of the bullets which can be fired from the gun per second?

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None of the above

$n = \frac{F}{m v^{2}}$

$n = \frac{F}{m v}$

$n = \sqrt{\frac{F}{m v}}$

answer is A.

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Detailed Solution

$T h e c h a n g e i n m o m e n t u m o f e a c h b u l l e t ∆ P = m (v - u) . A s u = 0, ∆ P = m v . I f n i s t h e n u m b e r o f b u l l e t s f i r e d p e r s e c o n d, t h e n r a t e o f c h a n g e o f m o m e n t u m o f t h e g u n \frac{∆ P}{∆ t} = n m v T h u s b y N e w t o n' s s e c o n d l a w F = \frac{∆ P}{∆ t} = n m v n = \frac{F}{m v}$