Assertion: A particle follows only a parabolic path if acceleration is constant.
Reason : In projectile motion path is parabolic, as acceleration is assumed to be constant at low heights.

Options

A. (a)If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b)If both Assertion and Reason are true and the Reason is not the correct explanation of the Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (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 provided.

### Step 1: Analyze the Assertion
The assertion states: "A particle follows only a parabolic path if acceleration is constant."

- When we consider motion under constant acceleration, such as free fall under gravity, the trajectory can be linear (straight line) if the motion is vertical (like dropping a ball straight down).
- Thus, the assertion is incorrect because constant acceleration does not necessarily imply a parabolic path; it can also result in a straight line path.

### Step 2: Analyze the Reason
The reason states: "In projectile motion, the path is parabolic, as acceleration is assumed to be constant at low heights."

- In projectile motion, the only force acting on the projectile after it is launched is gravity (assuming air resistance is negligible).
- The acceleration due to gravity (g) is considered constant for small heights above the Earth's surface. This leads to a parabolic trajectory.
- Therefore, the reason is correct because it accurately describes the nature of projectile motion under the assumption of constant acceleration.

### Step 3: Conclusion
Based on the analysis:
- The assertion is false because constant acceleration does not exclusively lead to a parabolic path.
- The reason is true because projectile motion does indeed follow a parabolic path when acceleration due to gravity is assumed constant.

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

### Final Answer
The assertion is false, and the reason is true. Therefore, the correct option is D.

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