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Q.
A machine gun fires $360$ bullets per minute, with a velocity of $600\, ms ^{-1}$. If the power of the gun is $5.4\, kW$, then mass of each bullet is
Work, Energy and Power
Solution:
Here, $n=\frac{360}{60}=6 \text{bullets} s^{-1}$
Velocity, $v=600\, ms ^{-1}, m=$ ?
Power of gun = Power of bullets
$5.4 \times 10^{3}=\frac{1}{2}( nm ) v^{2}$
$2 \times 5400=6 \times m(600)^{2}$
$\Rightarrow m =\frac{2 \times 5400}{6 \times 600 \times 600} kg$
$=\frac{1}{200} kg =\frac{1000}{200} g =5\, g$