The height of a swing changes during its motion from 0.1 m to 2.5 m . The minimum velocity of a boy who swings in this swing is

Options

A. 5.4 m/s
B. 4.95 m/s
C. 3.14 m/s
D. zero

Answer

To find the minimum velocity of a boy swinging on a swing that changes height from 0.1 m to 2.5 m, we can analyze the situation using the principles of simple harmonic motion (SHM).

### Step-by-Step Solution:

1. **Understand the Motion of the Swing**:
The swing moves back and forth, and its height changes from 2.5 m (highest point) to 0.1 m (lowest point). The swing's motion can be modeled as simple harmonic motion.

2. **Identify the Extreme Positions**:
In SHM, the extreme positions are where the velocity is minimum (which is zero at the highest points) and the maximum velocity occurs at the equilibrium position (the lowest point).

3. **Determine the Minimum Velocity**:
At the extreme positions (2.5 m and 0.1 m), the swing momentarily stops before changing direction. Therefore, at these points, the velocity is zero.

4. **Conclusion**:
The minimum velocity of the boy swinging in the swing occurs at the extreme positions, which is zero.

Thus, the minimum velocity of the boy who swings in this swing is **0 m/s**.

### Final Answer:
The minimum velocity of the boy is **0 m/s**.

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