A gun fire bullets each of mass 1 g with velocity of `10 ms ^(-1)` by exerting a constant force of 5 g weight. Then , the number of bullets fired per second is (take g = `10 ms ^(-2)` )

Options

A. 50
B. 5
C. 10
D. 25

Answer

To solve the problem step by step, we need to determine how many bullets are fired per second by the gun, given the mass of each bullet, its velocity, and the force exerted by the gun.

### Step 1: Understand the Given Data
- Mass of each bullet (m) = 1 g = 1/1000 kg = 0.001 kg
- Velocity of each bullet (v) = 10 m/s
- Force exerted by the gun (F) = 5 g weight = 5 g = 5 × 10^-3 kg × g = 5 × 10^-3 kg × 10 m/s² = 0.05 N

### Step 2: Calculate the Change in Momentum for One Bullet
The momentum (p) of a bullet is given by the formula:
\[ p = m \cdot v \]
For one bullet:
\[ p = 0.001 \, \text{kg} \cdot 10 \, \text{m/s} = 0.01 \, \text{kg m/s} \]

### Step 3: Relate Force to Change in Momentum
According to Newton's second law, the force is equal to the rate of change of momentum:
\[ F = \frac{\Delta p}{\Delta t} \]
Where \( \Delta p \) is the change in momentum and \( \Delta t \) is the time interval.

### Step 4: Express Change in Momentum for n Bullets
If n bullets are fired per second, the total change in momentum per second is:
\[ \Delta p = n \cdot (0.01 \, \text{kg m/s}) \]

### Step 5: Set Up the Equation
Now, substituting into the force equation:
\[ F = n \cdot (0.01) \]
We know that \( F = 0.05 \, \text{N} \), so we can set up the equation:
\[ 0.05 = n \cdot 0.01 \]

### Step 6: Solve for n
To find n, rearrange the equation:
\[ n = \frac{0.05}{0.01} = 5 \]

### Conclusion
The number of bullets fired per second is **5**.

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