A : When a body moves in a circle the work done by the centripetal force is always zero.
R : Centripetal force is perpendicular to displacement at every instant.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are falsė statements, then mark (4).

Answer

To solve the problem, we need to analyze the assertion (A) and the reason (R) provided in the question.

### Step 1: Understanding the Assertion
The assertion states that "When a body moves in a circle, the work done by the centripetal force is always zero."

**Explanation:**
Work done (W) is defined as the dot product of force (F) and displacement (s), given by the formula:
\[ W = F \cdot s = F \cdot s \cdot \cos(\theta) \]
where \( \theta \) is the angle between the force and the displacement vector.

### Step 2: Analyzing the Centripetal Force
In circular motion, the centripetal force always acts towards the center of the circle.

**Key Point:** The direction of the centripetal force is always perpendicular to the direction of the displacement of the body moving along the circular path.

### Step 3: Calculating the Work Done
Since the centripetal force is perpendicular to the displacement at every instant, we can conclude:
- The angle \( \theta \) between the centripetal force and the displacement is 90 degrees.
- Therefore, \( \cos(90^\circ) = 0 \).

Using the work formula:
\[ W = F \cdot s \cdot \cos(90^\circ) = F \cdot s \cdot 0 = 0 \]

Thus, the work done by the centripetal force is indeed zero.

### Step 4: Understanding the Reason
The reason states that "Centripetal force is perpendicular to displacement at every instant."

**Explanation:**
This statement is true because, in uniform circular motion, the direction of the velocity (and hence the displacement) is tangential to the circle, while the centripetal force is directed radially inward towards the center of the circle. Since these two directions are perpendicular, the reason correctly explains the assertion.

### Conclusion
Both the assertion (A) and the reason (R) are true, and the reason is a correct explanation of the assertion.

### Final Answer:
Both assertion and reason are true, and the reason is the correct explanation of the assertion.

---