Question

A machine gun fires 300 bullets per minute. If the mass of each bullet is \(10g\) and the velocity of the bullets is \(600 { m/s}\), the power (in kW) of the gun is:

• A. \(43200\)
• B. \(9\)
• C. \(72\)
• D. \(7.2\)

Hint:

Power is calculated as the rate of kinetic energy: \[ P = \frac{1}{2} m v^2 \times {bullets per second} \] Always convert mass to kg and time to seconds.

Answer 1

The Correct Option is B

Step 1: Understanding Power Calculation The power of the gun is given by the rate of change of kinetic energy: \[ P = \frac{\Delta KE}{\Delta t} \] The kinetic energy of a single bullet is: \[ KE = \frac{1}{2} m v^2 \] where: \( m = 10g = 10 \times 10^{-3} { kg} \) (mass of one bullet), \( v = 600 { m/s} \) (velocity of bullet). 
Step 2: Finding the Kinetic Energy of One Bullet \[ KE = \frac{1}{2} \times (10 \times 10^{-3}) \times (600)^2 \] \[ = \frac{1}{2} \times 0.01 \times 360000 \] \[ = \frac{3600}{2} = 1800 { J} \] 
Step 3: Finding Power Output The gun fires 300 bullets per minute, i.e., 5 bullets per second: \[ P = 5 \times 1800 \] \[ = 9000 { W} = 9 { kW} \] Thus, the correct answer is: \[ P = 9 { kW} \]