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:

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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.
Updated On: May 28, 2025
  • \( 3.6 \, \text{kW} \)
  • \( 3 \, \text{kW} \)
  • \( 5.4 \, \text{kW} \)
  • \( 2.5 \, \text{kW} \)
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The Correct Option is D

Approach Solution - 1

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).
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Approach Solution -2

Step 1: Understand what is being asked.
We are asked to calculate the power of the machine gun, which relates to the rate at which work is done or energy is transferred.

Step 2: Identify the given data.
- Number of bullets per minute = 300
- Velocity of each bullet = 500 m/s
- Mass of each bullet = 4 g = 0.004 kg

Step 3: Use the formula for kinetic energy of a bullet.
Kinetic energy of one bullet:
\[ KE = \frac{1}{2}mv^2 = \frac{1}{2} \times 0.004 \times (500)^2 = 0.002 \times 250000 = 500 \, \text{J} \]

Step 4: Find total energy per minute.
Energy per minute = \( 300 \times 500 = 150000 \, \text{J} \)

Step 5: Convert to power (energy per second).
Power = Energy / Time = \( \frac{150000}{60} = 2500 \, \text{W} = 2.5 \, \text{kW} \)

Final Answer:
\[ \boxed{2.5 \, \text{kW}} \]
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