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 question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding Power**:
Power (P) is defined as the rate at which work is done or energy is transferred. Mathematically, it can be expressed as:
\[ P = \mathbf{F} \cdot \mathbf{v} = Fv \cos \theta \]
where \( \mathbf{F} \) is the force, \( \mathbf{v} \) is the velocity, and \( \theta \) is the angle between the force and the velocity vectors.

**Hint**: Remember that power depends on the angle between force and velocity.

2. **Projectile Motion Analysis**:
In projectile motion, the only force acting on the body is the gravitational force, which acts downward. The velocity of the projectile has two components: horizontal (x-direction) and vertical (y-direction). At the maximum height of the projectile, the vertical component of the velocity becomes zero, and only the horizontal component remains.

**Hint**: Identify the point in projectile motion where the vertical velocity is zero.

3. **Power of Gravitational Force**:
At the maximum height, the gravitational force (downward) and the velocity (horizontal) are perpendicular to each other. Therefore, the angle \( \theta \) between the force and velocity is 90 degrees (\( \pi/2 \)):
\[ \cos(90^\circ) = 0 \]
Thus, the power delivered by the gravitational force at this point is:
\[ P = Fv \cos(90^\circ) = 0 \]
This confirms that the power of the gravitational force on the body in projectile motion is zero at least once during its motion.

**Hint**: Recall that power is zero when the angle between force and velocity is 90 degrees.

4. **Vertical Circle Analysis**:
Now, consider a body moving in a vertical circle. The tension in the wire acts towards the center of the circle, while the velocity of the body is tangential to the circle. At any point in the vertical circle, the tension (T) and the velocity (v) are also perpendicular to each other.

**Hint**: Visualize the forces acting on the body in a vertical circle.

5. **Power Delivered by Tension**:
Since the angle \( \theta \) between the tension and the velocity is always 90 degrees, we have:
\[ P = T v \cos(90^\circ) = 0 \]
This means that the power delivered by the tension in the wire to the body in a vertical circle is always zero.

**Hint**: Remember that power is zero when the force (tension) and the velocity are perpendicular.

6. **Conclusion**:
Both the assertion (A) and the reason (R) are correct. The assertion states that the power of the gravitational force on a body in projectile motion is zero at its maximum height, and the reason states that the power delivered by the tension in the wire to a body in a vertical circle is always zero. Therefore, both statements are true, but the reason does not explain the assertion.

**Final Answer**: Both A and R are correct, but R is not the correct explanation for A.