Question

A machine gun with power 15 kW can fire 360 bullets per minute. If the mass of each bullet is 5 g, then the velocity of the bullets is:

• A. 1500 m s$^{-1}$
• B. 1000 m s$^{-1}$
• C. 3600 m s$^{-1}$
• D. 500 m s$^{-1}$

Hint:

Power is energy per unit time. Equate the energy per bullet to its kinetic energy to find velocity.

Answer 1

The Correct Option is B

Power of the gun is 15 kW = 15000 W. 
Bullets fired per second: $ \frac{360}{60} = 6 $. 
Energy per bullet: \[ {Energy} = \frac{15000}{6} = 2500 \, {J} \] Mass of each bullet is 5 g = 0.005 kg. Kinetic energy of a bullet: \[ 2500 = \frac{1}{2} \times 0.005 \times v^2 \implies 2500 = 0.0025 v^2 \implies v^2 = 1000000 \implies v = 1000 \, {m s}^{-1} \] Thus, the velocity is 1000 m s$^{-1}$, matching option (2).