Q122 / 180 · JIPMER 2018 · Physics

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

  • A
    $5 kg$
  • B
    $0.5 kg$
  • Correct answer
    C
    $5 g$
  • D
    $0.5 g$

Solution

Here, $\mathrm{n}=\frac{360}{60}=6$ bullets s ${ }^{-1}$ Velocity, $\mathrm{v}=600 \mathrm{~ms}^{-1}, \mathrm{~m}=$ ? Power of gun = Power of bullets $5.4 \times 10^3=\frac{1}{2}(\mathrm{~nm}) \mathrm{v}^2$ $2 \times 5400=6 \times \mathrm{m}(600)^2$ or $\quad \begin{aligned} \mathrm{m} & =\frac{2 \times 5400}{6 \times 600 \times 600} \mathrm{~kg} \\ & =\frac{1}{200} \mathrm{~kg}=\frac{1000}{200} \mathrm{~g}=5 \mathrm{~g}\end{aligned}$

Hence, the correct answer is option: 'C'.

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