A short magnet is allowed to fall along the axis of a horizontal metalic ring. Starting from rest, the distance fallen by the magnet in one second may be

Options

A. `4m`
B. `5m`
C. `6m`
D. `7m`

Explanation

To solve the problem of how far a short magnet falls in one second when allowed to fall along the axis of a horizontal metallic ring, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a short magnet falling through a horizontal metallic ring. The magnet starts from rest.

2. **Forces Acting on the Magnet**:
- As the magnet falls, it will experience gravitational force acting downward, which is equal to \( mg \) (where \( m \) is the mass of the magnet and \( g \) is the acceleration due to gravity).
- However, due to electromagnetic induction, the falling magnet will induce a current in the metallic ring, which creates an upward magnetic force opposing the fall of the magnet.

3. **Net Acceleration**:
- Because of the opposing force from the induced current, the net acceleration \( a \) of the magnet will be less than \( g \). Therefore, we can say:
\[ a < g \]
- For simplicity, we can assume \( a \approx g \) for a short time, but we must remember that it will actually be less.

4. **Calculating Distance Fallen**:
- The formula for distance fallen under constant acceleration is:
\[ S = ut + \frac{1}{2} a t^2 \]
- Since the magnet starts from rest, \( u = 0 \). Thus, the equation simplifies to:
\[ S = \frac{1}{2} a t^2 \]
- Substituting \( t = 1 \) second, we get:
\[ S = \frac{1}{2} a (1)^2 = \frac{1}{2} a \]

5. **Estimating the Distance**:
- If we assume \( g \approx 10 \, \text{m/s}^2 \), then:
\[ S = \frac{1}{2} \cdot 10 = 5 \, \text{meters} \]
- However, since the actual acceleration \( a \) is less than \( g \), the distance \( S \) will be less than 5 meters.

6. **Final Conclusion**:
- Since the distance fallen by the magnet must be less than 5 meters, we can estimate that the distance fallen in one second could be around 4 meters or less.

### Answer:
The distance fallen by the magnet in one second may be approximately **4 meters** or less.