Question

A machine gun fires $360$ bullets per minute, with a velocity of $600m{s}^{-1}$. If the power of the gun is $5.4kW$, then mass of each bullet is

• A. 5 kg
• B. 0.5 kg
• C. 5 g
• D. 0.5 g

Answer 1

Answer: (C)

Here, $n=\frac{360}{60}=6\text{bullets}{s}^{-1}$
Velocity, $v=600m{s}^{-1},m=$ ?
Power of gun = Power of bullets
$5.4\times 10^3=\frac{1}{2}(nm)v^2$
$2\times 5400=6\times m(600{)}^2$
$\Rightarrow m=\frac{2\times 5400}{6\times 600\times 600}kg$
$=\frac{1}{200}kg=\frac{1000}{200}g=5g$