A boy is rotating in a circular motion, a stone of mass 500 g by using a string of length 50 cm with a speed 10 cm/s. What will be the work done by the force applied by the boy?

Options

A. `0 . 0 1 pi J`
B. ` pi J`
C. ` 10 pi J`
D. Zero

Explanation

To solve the problem of the work done by the force applied by the boy while rotating a stone in circular motion, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the System**:
- A boy is rotating a stone of mass 500 g (which is 0.5 kg) using a string of length 50 cm (which is 0.5 m) at a speed of 10 cm/s (which is 0.1 m/s).

2. **Identify the Type of Motion**:
- The stone is in uniform circular motion. In this type of motion, the speed of the stone remains constant, but its direction changes continuously.

3. **Determine the Force Acting on the Stone**:
- The force that keeps the stone moving in a circle is called the centripetal force. This force is directed towards the center of the circular path.

4. **Analyze the Work Done by the Force**:
- Work done (W) is calculated using the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where:
- \(F\) is the force applied,
- \(d\) is the displacement,
- \(\theta\) is the angle between the force and the direction of displacement.

5. **Determine the Angle**:
- In circular motion, the tension (force applied by the boy) acts towards the center of the circle, while the displacement of the stone at any point is tangential to the circle. Therefore, the angle \(\theta\) between the tension force and the displacement is 90 degrees.

6. **Calculate the Work Done**:
- Since \(\cos(90^\circ) = 0\), the work done by the centripetal force (tension) is:
\[ W = F \cdot d \cdot \cos(90^\circ) = F \cdot d \cdot 0 = 0 \]

7. **Conclusion**:
- The total work done by the force applied by the boy is zero.

### Final Answer:
The work done by the force applied by the boy is **0 Joules**.

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