A machine gun fires 360 bullets per minute, with a velocity of `600 ms^(-1)`.If the power of the gun is 5.4 kW then mass of each bullet is

Options

A. 5kg
B. 0.5 kg
C. 5g
D. 0.5g

Answer

To find the mass of each bullet fired by the machine gun, we can follow these steps:

### Step 1: Understand the Given Data
- Number of bullets fired per minute (N) = 360 bullets/minute
- Velocity of each bullet (V) = 600 m/s
- Power of the gun (P) = 5.4 kW = 5400 W

### Step 2: Convert Bullets per Minute to Bullets per Second
Since power is typically calculated in terms of seconds, we convert the number of bullets fired per minute to bullets per second:
\[ N = \frac{360 \text{ bullets}}{60 \text{ seconds}} = 6 \text{ bullets/second} \]

### Step 3: Calculate the Total Kinetic Energy of the Bullets Fired in One Second
The kinetic energy (KE) of a single bullet is given by the formula:
\[ KE = \frac{1}{2} m V^2 \]
For N bullets, the total kinetic energy per second (which is the power) can be expressed as:
\[ \text{Total KE} = N \times \frac{1}{2} m V^2 \]
Substituting N = 6 bullets/second:
\[ \text{Total KE} = 6 \times \frac{1}{2} m (600)^2 \]
\[ \text{Total KE} = 6 \times \frac{1}{2} m \times 360000 \]
\[ \text{Total KE} = 6 \times 180000 m = 1080000 m \text{ Joules/second} \]

### Step 4: Relate Power to Kinetic Energy
Power is defined as the rate of doing work or the rate of energy transfer. Therefore, we can set the total kinetic energy equal to the power:
\[ P = \text{Total KE} \]
\[ 5400 = 1080000 m \]

### Step 5: Solve for the Mass of Each Bullet
Rearranging the equation to solve for m:
\[ m = \frac{5400}{1080000} \]
\[ m = \frac{54}{10800} \]
\[ m = \frac{1}{2000} \]
\[ m = 0.0005 \text{ kg} \]
Converting kg to grams:
\[ m = 0.0005 \times 1000 = 5 \text{ grams} \]

### Conclusion
The mass of each bullet is **5 grams**.

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