Assertion : Simple harmonic motion is an example on one dimensional motion with non-uniform acceleration .
Reason : In simple harmonic motion, acceleration varies with displacement linearly.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but 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: "Simple harmonic motion is an example of one-dimensional motion with non-uniform acceleration."

- **Understanding Simple Harmonic Motion (SHM)**:
- SHM can occur in one dimension (like a mass on a spring) or in two dimensions (like a pendulum swinging in a circular path).
- Therefore, the assertion that SHM is only one-dimensional is incorrect.

### Step 2: Analyze the Reason
The reason states: "In simple harmonic motion, acceleration varies with displacement linearly."

- **Understanding the Relationship**:
- The formula for acceleration in SHM is given by \( a = -\omega^2 x \), where \( \omega \) is the angular frequency and \( x \) is the displacement.
- This indicates that acceleration is directly proportional to displacement, but with a negative sign, indicating that the acceleration is directed towards the equilibrium position.
- This relationship shows that acceleration does vary linearly with displacement.

### Step 3: Conclusion
- The assertion is **false** because SHM can be two-dimensional.
- The reason is **true** because acceleration does vary linearly with displacement in SHM.

### Final Answer
- Assertion: False
- Reason: True