Assertion : The graph of potential energy and kinetic energy of a particle in SHM with respect to position is a parabola.
Reason : Potential energy and kinetic energy do not vary linearly with position.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**: The assertion states that "The graph of potential energy and kinetic energy of a particle in SHM with respect to position is a parabola."

- In Simple Harmonic Motion (SHM), the potential energy (U) is given by the formula:
\[ U = \frac{1}{2} k x^2 \]
where \(k\) is the spring constant and \(x\) is the displacement from the mean position. This equation is quadratic in nature, which means that if we plot potential energy against position, we will get a parabolic curve.

2. **Understanding the Kinetic Energy**: The kinetic energy (K) of the particle in SHM is given by:
\[ K = \frac{1}{2} m v^2 \]
where \(v\) is the velocity of the particle. The velocity in SHM can be expressed as:
\[ v = \omega \sqrt{A^2 - x^2} \]
where \(A\) is the amplitude and \(\omega\) is the angular frequency. Substituting this into the kinetic energy formula gives:
\[ K = \frac{1}{2} m \omega^2 (A^2 - x^2) \]
This also results in a quadratic relationship with respect to position \(x\), indicating that kinetic energy also varies quadratically.

3. **Conclusion on the Assertion**: Since both potential energy and kinetic energy vary as the square of the position, the assertion is correct. The graphs of both energies with respect to position will indeed be parabolic.

4. **Understanding the Reason**: The reason states that "Potential energy and kinetic energy do not vary linearly with position."

- This statement is also correct because both energies are quadratic functions of position, which means they do not change in a linear manner.

5. **Evaluating the Relationship**: While both the assertion and reason are true, the reason does not directly explain why the graph of potential and kinetic energy is parabolic. The reason simply states that they do not vary linearly, but it does not address the specific form of the quadratic relationship.

6. **Final Answer**: Therefore, both the assertion and reason are true, but the reason is not the correct explanation for the assertion. Hence, the answer is option B: "Both assertion and reason are true, but reason is not the correct explanation of assertion."