Assertion: Circular and projectile motions both are two idimensional motion.But In circular motion, we cannot apply `v=u+at` directly, whereas in projectile motion we can.
Reason: Projectile motion takes place under gravity, while in circular motion gravity has no role.

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 but Reason is not the correct explanation of Assertion.
C. If Assertion is true, true but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the question, we need to analyze both the assertion and the reason given in the problem.

### Step 1: Analyze the Assertion
The assertion states that both circular motion and projectile motion are two-dimensional motions, but we cannot apply the equation \( v = u + at \) directly in circular motion.

- **In Circular Motion**:
- When an object moves in a circular path, it experiences centripetal acceleration directed towards the center of the circle. If the speed is constant, the acceleration is centripetal only. If the speed varies, there is also tangential acceleration.
- The acceleration is not constant in general because it can change direction and magnitude depending on the speed and radius of the circular path.
- The equation \( v = u + at \) is applicable only for uniformly accelerated linear motion where acceleration is constant. Since circular motion can involve variable acceleration, this equation cannot be directly applied.

### Step 2: Analyze the Reason
The reason states that projectile motion occurs under the influence of gravity, while gravity has no role in circular motion.

- **In Projectile Motion**:
- The motion is indeed influenced solely by gravity, which acts downwards. This results in a constant acceleration (g) in the vertical direction.
- The horizontal motion is uniform, and the vertical motion is uniformly accelerated due to gravity. Thus, the equation \( v = u + at \) can be applied.

- **In Circular Motion**:
- The statement that gravity has no role is incorrect. In vertical circular motion, gravity plays a significant role as it contributes to the centripetal force required to keep the object in circular motion.
- For example, in a vertical loop, both tension and gravitational force act on the object, affecting its motion.

### Conclusion
- The assertion is true because we cannot apply \( v = u + at \) in circular motion due to the nature of acceleration.
- The reason is false because gravity does play a role in certain types of circular motion.

### Final Answer
The correct conclusion is that the assertion is true, but the reason is false. Therefore, the answer is option C.

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