A : Power delivered by the tension in the wire to a body in vertical circle is always zero.
R : Tension in the wire is equal to the centripetail force acting on the body doing vertical circular motion.

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, we will analyze both the assertion (A) and the reason (R) provided in the statement.

### Step 1: Analyze the Assertion (A)
The assertion states that "Power delivered by the tension in the wire to a body in vertical circle is always zero."

1. **Understanding Power**: Power (P) is defined as the rate at which work is done, which can also be expressed as the dot product of force (F) and velocity (v):
\[ P = F \cdot v = Fv \cos(\theta) \]
where \(\theta\) is the angle between the force and the direction of velocity.

2. **Direction of Tension and Velocity**: In vertical circular motion, the tension in the wire acts towards the center of the circle (radially inward), while the velocity of the body is tangential to the circle.

3. **Angle Between Tension and Velocity**: The angle \(\theta\) between the tension (T) and the velocity (v) is always 90 degrees because they are perpendicular to each other.

4. **Calculating Power**: Since \(\cos(90^\circ) = 0\), the power delivered by the tension is:
\[ P = T v \cos(90^\circ) = T v \cdot 0 = 0 \]
Therefore, the assertion is true.

### Step 2: Analyze the Reason (R)
The reason states that "Tension in the wire is equal to the centripetal force acting on the body doing vertical circular motion."

1. **Understanding Centripetal Force**: The centripetal force required to keep an object moving in a circle is given by:
\[ F_c = \frac{mv^2}{r} \]
where \(m\) is the mass of the object, \(v\) is its tangential speed, and \(r\) is the radius of the circular path.

2. **Forces Acting on the Body**: In vertical circular motion, the forces acting on the body at the lowest point include:
- The tension (T) in the wire acting upwards.
- The weight (mg) of the body acting downwards.

3. **Net Force for Circular Motion**: The net force providing the centripetal acceleration is the difference between the tension and the weight:
\[ T - mg = \frac{mv^2}{r} \]
This shows that the tension is not equal to the centripetal force alone; rather, it is the net force that provides the centripetal acceleration.

4. **Conclusion on Reason**: Since tension is not equal to the centripetal force (it includes the weight of the body), the reason is false.

### Final Conclusion
- The assertion (A) is true: Power delivered by the tension in the wire to a body in vertical circular motion is always zero.
- The reason (R) is false: Tension in the wire is not equal to the centripetal force acting on the body.

Thus, the correct answer is that the assertion is true and the reason is false.