Asseration : In circular motion work done by all the forces acting on the body is zero.
Reason : Centripetal force and veloity are mutually perpendicular.

Options

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

Explanation

To solve the assertion and reason question, we will analyze both statements step by step.

### Step 1: Analyze the Assertion
The assertion states: "In circular motion, the work done by all the forces acting on the body is zero."

- In uniform circular motion, the speed of the body remains constant, and the direction of the velocity changes continuously. The net force acting on the body is the centripetal force, which acts towards the center of the circular path.
- Work done is defined as the product of the force and the displacement in the direction of the force. Since the centripetal force is always directed towards the center and the displacement of the body is tangential to the circular path, the angle between the centripetal force and the displacement is 90 degrees.
- Therefore, the work done by the centripetal force is given by:
\[ W = F \cdot d \cdot \cos(\theta) = F \cdot d \cdot \cos(90^\circ) = 0 \]
- Thus, for uniform circular motion, the work done by the centripetal force is indeed zero. However, if the motion is non-uniform or if we consider other forces (like gravitational force in a vertical circle), the work done may not be zero.

**Conclusion for Assertion:** The assertion is partially true; it is true for uniform circular motion but not for all cases of circular motion.

### Step 2: Analyze the Reason
The reason states: "Centripetal force and velocity are mutually perpendicular."

- In uniform circular motion, the velocity vector is tangential to the circular path, while the centripetal force is directed towards the center of the circle. This means that they are indeed perpendicular to each other.
- However, in cases such as vertical circular motion, the direction of the velocity changes as the object moves along the circular path. At certain points (like the top or bottom of the circle), the centripetal force may not be perpendicular to the velocity.

**Conclusion for Reason:** The reason is true for uniform circular motion but not universally applicable to all cases of circular motion.

### Final Conclusion
- Both the assertion and reason are true only under specific conditions (uniform circular motion).
- Therefore, the assertion is not universally true, and the reason does not universally apply either.

### Final Answer
Both the assertion and reason are false in a general context, but true in specific cases (uniform circular motion).