Assertion (A): Centripetal force does no work .
Reason (R) : Force and displacement are perpendicular to each other

Options

A. If both A and R are true and R is the correct explanation of A.
B. If both A and R are true but R is not the correct explanation of A.
C. If A is true but R is false
D. If A is false but R is true.

Explanation

To solve the question, we need to analyze the assertion and the reason provided:

**Assertion (A): Centripetal force does no work.**
**Reason (R): Force and displacement are perpendicular to each other.**

### Step-by-Step Solution:

1. **Understanding Centripetal Force:**
- Centripetal force is the force that acts on an object moving in a circular path, directed towards the center of the circle.

2. **Direction of Motion:**
- When an object moves in a circular path, its velocity is tangential to the circle at any point. This means that the direction of motion is along the tangent to the circle.

3. **Analyzing the Angle Between Force and Displacement:**
- In the case of circular motion, the centripetal force acts towards the center of the circle, while the displacement (or the direction of motion) is tangential to the circle.
- Therefore, the angle (θ) between the centripetal force and the direction of displacement is 90 degrees (θ = 90°).

4. **Calculating Work Done:**
- The work done (W) by a force is given by the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \( F \) is the force, \( d \) is the displacement, and \( \theta \) is the angle between the force and the displacement.
- Since θ = 90°, we have:
\[ W = F \cdot d \cdot \cos(90°) = F \cdot d \cdot 0 = 0 \]
- This shows that the work done by the centripetal force is zero.

5. **Conclusion:**
- Since the centripetal force does no work and the reason provided (that force and displacement are perpendicular) correctly explains why the work done is zero, we can conclude that both the assertion and reason are true, and the reason is correctly explaining the assertion.

### Final Answer:
Both Assertion (A) and Reason (R) are true, and Reason (R) correctly explains Assertion (A).

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