A : Power of the gravitational force on the body in a projectile motion is zero, once during its motion.
R : Power delivered by the tension in the wire to a body in vertical circle is always zero.

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 both the assertion (A) and the reason (R) provided in the question.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that the power of the gravitational force on a body in projectile motion is zero at least once during its motion.
- Power (P) is defined as the dot product of force (F) and velocity (v):
\[ P = F \cdot v = |F| |v| \cos(\theta) \]
where \(\theta\) is the angle between the force and the velocity vectors.

2. **Identifying the Condition for Zero Power**:
- For power to be zero, the term \(F \cdot v\) must equal zero. This occurs when \(\cos(\theta) = 0\), which means \(\theta = 90^\circ\). This indicates that the force is perpendicular to the velocity.

3. **Analyzing Projectile Motion**:
- In projectile motion, at the maximum height, the vertical component of the velocity is zero, and the object only has horizontal motion.
- At this point, the gravitational force acts downward (negative y-direction), while the velocity is horizontal (positive x-direction). Thus, the angle between the gravitational force and the velocity is \(90^\circ\).

4. **Conclusion for Assertion**:
- Since the gravitational force is perpendicular to the velocity at the maximum height, the power delivered by the gravitational force is indeed zero at this point. Therefore, the assertion (A) is true.

5. **Understanding the Reason (R)**:
- The reason states that the power delivered by the tension in the wire to a body in vertical circular motion is always zero.
- In vertical circular motion, the tension force acts along the radius of the circle, while the velocity of the body is tangential to the circle.

6. **Identifying the Condition for Tension**:
- At any point in the vertical circle, the angle between the tension (which acts radially) and the velocity (which is tangential) is \(90^\circ\).
- Therefore, using the same power formula:
\[ P = T \cdot v = |T| |v| \cos(90^\circ) = 0 \]
- This shows that the power delivered by the tension is also zero at all points in the vertical circle.

7. **Conclusion for Reason**:
- The reason (R) is also true, as the tension is always perpendicular to the velocity in vertical circular motion.

8. **Final Evaluation**:
- Both the assertion (A) and the reason (R) are true. However, the reason does not explain the assertion directly, as they pertain to different scenarios (projectile motion vs. vertical circular motion).

### Final Answer:
- The correct option is that both the assertion and reason are true, but the reason is not the correct explanation of the assertion.