A: If length of a spring is halved, then its force constant becomes double.
R: The spring constant is inversely proportional to length of spring.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the assertion and reason question regarding the relationship between the length of a spring and its spring constant (force constant), we will follow these steps:

### Step 1: Understand the Assertion
The assertion states: "If the length of a spring is halved, then its force constant becomes double."

### Step 2: Understand the Reason
The reason states: "The spring constant is inversely proportional to the length of the spring."

### Step 3: Recall the Relationship
The spring constant \( K \) is related to the length \( L \) of the spring by the formula:
\[ K \propto \frac{1}{L} \]
This means that if the length of the spring decreases, the spring constant increases.

### Step 4: Analyze the Changes
If the original length of the spring is \( L \) and the original spring constant is \( K \), when the length is halved:
\[ L' = \frac{L}{2} \]

### Step 5: Apply the Inverse Proportionality
From the relationship \( K \cdot L = \text{constant} \), we can write:
\[ K \cdot L = K' \cdot L' \]
Substituting \( L' \):
\[ K \cdot L = K' \cdot \frac{L}{2} \]

### Step 6: Solve for the New Spring Constant
Rearranging the equation gives:
\[ K' = 2K \]
This indicates that the new spring constant \( K' \) is indeed double the original spring constant \( K \).

### Step 7: Conclusion
Since both the assertion and the reason are true, and the reason correctly explains the assertion, we conclude that:
- The assertion is true.
- The reason is true.
- The reason is a correct explanation of the assertion.

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

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