A disc of mass 5 kg is kept floating horizontally in mid air by firing 10 bullets per second vertically up. If the mass of each bullet is 50 gm and bullets rebound with same speed, the speed of each bullet is, (g = `10 ms^(-2)`)

Options

A. `100 ms^(-1)`
B. `200 ms^(-1)`
C. `50 ms^(-1)`
D. `10 ms^(-1)`

Answer

To solve the problem, we need to determine the speed of each bullet fired from a disc that is floating in mid-air. The disc has a mass of 5 kg and fires 10 bullets per second, with each bullet having a mass of 50 grams. The bullets rebound with the same speed they were fired. We will also use the acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \).

### Step-by-Step Solution:

1. **Convert the mass of the bullet to kilograms**:
\[ m = 50 \, \text{grams} = 50 \times 10^{-3} \, \text{kg} = 0.05 \, \text{kg} \]

2. **Calculate the total mass of bullets fired per second**:
Since 10 bullets are fired per second, the total mass of bullets fired per second is:
\[ \text{Total mass per second} = 10 \times m = 10 \times 0.05 \, \text{kg} = 0.5 \, \text{kg/s} \]

3. **Determine the weight of the disc**:
The weight of the disc, which acts downward, is given by:
\[ W = M \cdot g = 5 \, \text{kg} \times 10 \, \text{m/s}^2 = 50 \, \text{N} \]

4. **Set up the equation for equilibrium**:
For the disc to float, the upward force due to the bullets must equal the downward weight of the disc. The upward force can be expressed as the momentum change per second:
\[ F_{\text{up}} = \text{Total mass per second} \times v = 0.5 \, \text{kg/s} \times v \]
Setting this equal to the weight of the disc:
\[ 0.5 \, v = 50 \]

5. **Solve for the speed \( v \)**:
Rearranging the equation gives:
\[ v = \frac{50}{0.5} = 100 \, \text{m/s} \]

### Conclusion:
The speed of each bullet is \( 100 \, \text{m/s} \).