Question

A machine gun fires 300 bullets per minute each with a velocity of 500 ms\(^{-1}\). If the mass of each bullet is 4 g, the power of the machine gun is:

• A. \( 3.6 \, \text{kW} \)
• B. \( 3 \, \text{kW} \)
• C. \( 5.4 \, \text{kW} \)
• D. \( 2.5 \, \text{kW} \)

Hint:

To calculate the power, remember that the total energy is the sum of the kinetic energy of all the bullets, and the power is the rate at which this energy is delivered, which is the total energy divided by the time taken.

Answer 1

The Correct Option is D

The power is given by the work done per unit time. The work done for each bullet is the kinetic energy, which is given by: \[ KE = \frac{1}{2} mv^2 \] where \( m \) is the mass of the bullet and \( v \) is the velocity. The mass of each bullet is \( 4 \, \text{g} = 0.004 \, \text{kg} \) and the velocity is \( 500 \, \text{m/s} \). Thus, the kinetic energy of each bullet is: \[ KE = \frac{1}{2} \times 0.004 \times (500)^2 = 500000 \, \text{J} \] The total energy delivered by the machine gun in one minute (since 300 bullets are fired per minute) is: \[ \text{Total energy} = 300 \times 500000 = 150000000 \, \text{J} \] The power is the energy delivered per second. Since there are 60 seconds in a minute, the power is: \[ P = \frac{150000000}{60} = 2500000 \, \text{W} = 2.5 \, \text{kW} \] Thus, the power of the machine gun is \( 2.5 \, \text{kW} \). Hence, the correct answer is option (4).