Read the given statements and select the correct option.
Statement 1 :Potential energy of a stretched or compressed spring is directly proportional to square of extension or compression.
Statement 2 : Graph between potential energy of a spring versus the extension or compression of the spring is a straight line.

Options

A. Both statement 1 and statement 2 are true and statement 2 is the correct explanation of statement 1.
B. Both statement 1 and statement 2 are true but statement 2 is not the correct explanation of statement 1.
C. Statement 1 is true but statement 2 is false
D. Both statement 1 and statement 2 are false.

Explanation

To solve the question, we need to analyze the two statements provided:

**Statement 1:** The potential energy of a stretched or compressed spring is directly proportional to the square of extension or compression.

**Statement 2:** The graph between potential energy of a spring versus the extension or compression of the spring is a straight line.

### Step-by-Step Solution:

1. **Understanding Potential Energy in Springs:**
- The potential energy (U) stored in a spring when it is either stretched or compressed is given by the formula:
\[ U = \frac{1}{2} k x^2 \]
where \(k\) is the spring constant and \(x\) is the extension or compression from its equilibrium position.

2. **Analyzing Statement 1:**
- From the formula \(U = \frac{1}{2} k x^2\), we can see that potential energy (U) is indeed directly proportional to the square of the extension or compression (x).
- Therefore, **Statement 1 is true**.

3. **Analyzing Statement 2:**
- The relationship \(U = \frac{1}{2} k x^2\) indicates that if we plot potential energy (U) on the y-axis against extension or compression (x) on the x-axis, the graph will be a parabola (specifically, a quadratic curve) because of the \(x^2\) term.
- Hence, **Statement 2 is false** because the graph is not a straight line; it is a parabolic curve.

4. **Conclusion:**
- Since Statement 1 is true and Statement 2 is false, the correct option is that the first statement is true and the second statement is false.

### Final Answer:
The correct option is **Option 3** (Statement 1 is true, Statement 2 is false).

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