Question

A machine gun is mounted on a $200 \,kg$ vehicle on a horizontal smooth road (friction negligible). The gun fires $10$ bullets/s with a velocity of $500 \,ms$ lf the mass of each bullet be $10\, g$, what is the acceleration produced in the vehicle?

• A. $25 \,cm/s^{-2}$
• B. $25 \,m/s^{-2}$
• C. $50 \,cm/s^{-2}$
• D. $50 \,m/s^{-2}$

Answer 1

Answer: (A)

$25 \,cm/s^{-2}$

Answer 2

Momentum carried by each bullet $=m v$
$=0.010 \times 500 \,kg \,m / s$
$=5 \,kg m / s$
Now, force $=$ change in momentum in $1 s$
$= 5 \times 10$
$=50 \,N$
Hence, acceleration $=\frac{50}{200}\, m / s ^{2}$
$=25 \,cm / s ^{2}$