Assertion: The graph of total energy of a particle in SHM with respect to position is a straight line with zero slope.
Reason: Total energy of particle in SHM remains constant throughout its motion.

Options

A. If both assertion and reson 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.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided regarding the total energy of a particle in Simple Harmonic Motion (SHM).

### Step-by-Step Solution:

1. **Understanding SHM**: In SHM, a particle oscillates back and forth around an equilibrium position. The total mechanical energy (E) of the particle is the sum of its kinetic energy (KE) and potential energy (PE).

2. **Formulas for Energy**:
- The kinetic energy (KE) of a particle in SHM is given by:
\[ KE = \frac{1}{2} m v^2 \]
where \( v \) is the velocity of the particle.
- The potential energy (PE) in SHM is given by:
\[ PE = \frac{1}{2} k x^2 \]
where \( k \) is the spring constant and \( x \) is the displacement from the equilibrium position.

3. **Total Energy in SHM**: The total energy (E) in SHM is constant and is given by:
\[ E = KE + PE = \frac{1}{2} k A^2 \]
where \( A \) is the amplitude of the oscillation. This shows that the total energy does not depend on the position \( x \) of the particle.

4. **Graph of Total Energy**:
- Since the total energy \( E \) remains constant regardless of the position \( x \), if we plot a graph of total energy (y-axis) against position (x-axis), the graph will be a horizontal line.
- A horizontal line has a slope of zero, which confirms the assertion that the graph of total energy with respect to position is a straight line with zero slope.

5. **Evaluating the Reason**: The reason states that the total energy of the particle in SHM remains constant throughout its motion. This is indeed true, as derived from the equations above.

6. **Conclusion**: Both the assertion and the reason are true. Furthermore, the reason correctly explains the assertion, as the constancy of total energy leads to the graph being a straight line with zero slope.

### Final Answer:
Both the assertion and the reason are true, and the reason is the correct explanation of the assertion.

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