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 question regarding the work done by centripetal force when a body moves in a circle, we will analyze the assertion (A) and the reason (R) step by step.

### Step 1: Understanding the Assertion (A)
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 product of the force (F) applied on an object and the displacement (S) of that object in the direction of the force. Mathematically, it can be expressed as:
\[ W = F \cdot S = F \cdot S \cos(\theta) \]
where \(\theta\) is the angle between the force and the displacement vector.

### Step 2: Analyzing the Centripetal Force
Centripetal force acts towards the center of the circular path.

- **Direction of Centripetal Force**: As the body moves in a circle, the centripetal force (F_c) is always directed radially inward, towards the center of the circle.

### Step 3: Understanding the Displacement
The displacement of the body (ds) at any instant is tangential to the circular path.

- **Direction of Displacement**: At any point on the circular path, the displacement vector (ds) is tangent to the circle, meaning it is perpendicular to the radius (and hence to the centripetal force).

### Step 4: Determining the Work Done
Since the centripetal force is always perpendicular to the displacement, we can analyze the work done.

- **Calculating Work Done**: Since the angle \(\theta\) between the centripetal force and the displacement is 90 degrees, we have:
\[ W = F_c \cdot ds \cdot \cos(90^\circ) = F_c \cdot ds \cdot 0 = 0 \]
Therefore, the work done by the centripetal force is indeed zero.

### Step 5: Understanding the Reason (R)
The reason states that "centripetal force is perpendicular to displacement at every instant."

- **Verification of Reason**: As established, the centripetal force always acts towards the center of the circle, while the displacement is tangential to the circle. Thus, the reason is also correct.

### Conclusion
Both the assertion (A) and the reason (R) are correct, and the reason correctly explains why the work done by the centripetal force is zero.

### Final Answer
Both A and R are correct, and R is the correct explanation for A.

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