Q. Statement I: The total energy of a particle performing simple harmonic motion could be negative. Statement II: Potential energy of a system could be magnetic.

Options

A. Statement I is true statement II is true, Statement II is a correct explanation for Statement I.
B. Statement I is true statement II is true, Statement II is NOT a correct explanation for Statement I.
C. Statement I is true, Statement II is false
D. Statement I is false, Statement II is true

Explanation

To solve the question, we will analyze both statements separately and determine their validity.

### Step 1: Analyzing Statement I
**Statement I:** The total energy of a particle performing simple harmonic motion could be negative.

- In simple harmonic motion (SHM), the total mechanical energy \(E\) is given by the sum of kinetic energy \(K\) and potential energy \(U\):
\[ E = K + U \]
- The kinetic energy \(K\) is always non-negative (\(K \geq 0\)).
- The potential energy \(U\) can take on negative values depending on the reference point chosen for zero potential energy. For example, if we set the zero point of potential energy at a certain position, the potential energy can be negative when the particle is below that reference point.
- If the minimum potential energy \(U_{\text{min}}\) is negative and its absolute value is greater than the maximum kinetic energy \(K_{\text{max}}\), then the total energy \(E\) can indeed be negative.

**Conclusion for Statement I:** True

### Step 2: Analyzing Statement II
**Statement II:** Potential energy of a system could be magnetic.

- Potential energy can arise from various forces, including gravitational, elastic, and magnetic forces.
- Magnetic potential energy is indeed a valid concept. For example, in the case of magnetic fields, charged particles have potential energy associated with their positions in the field.
- Therefore, it is correct to say that potential energy can be magnetic.

**Conclusion for Statement II:** True

### Step 3: Evaluating the Relationship Between the Statements
- Statement I is true, and Statement II is also true.
- However, Statement II does not provide a direct explanation for Statement I. The total energy being negative is a consequence of the potential energy being negative in certain configurations, but it does not specifically relate to magnetic potential energy.

### Final Conclusion
- The correct answer is that both statements are true, but Statement II is not a correct explanation for Statement I.

### Answer:
**Option 2:** Statement I is True, Statement II is True, but Statement II is not a correct explanation for Statement I.

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