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 question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that if the length of a spring is halved, then its force constant (spring constant, k) becomes double.
- Mathematically, if the original length of the spring is L, and we halve it to L/2, we need to find the relationship between the spring constant k and the length L.

2. **Understanding the Spring Constant**:
- The spring constant (k) is related to the material properties of the spring and its dimensions. The formula for the spring constant k is given by:
\[ k = \frac{AE}{L} \]
where A is the cross-sectional area, E is the modulus of elasticity, and L is the length of the spring.

3. **Analyzing the Effect of Halving the Length**:
- If we halve the length of the spring, we substitute L with L/2 in the formula:
\[ k' = \frac{AE}{L/2} = \frac{2AE}{L} = 2k \]
- This shows that when the length is halved, the new spring constant (k') becomes double the original spring constant (k). Therefore, the assertion is correct.

4. **Understanding the Reason (R)**:
- The reason states that the spring constant is inversely proportional to the length of the spring.
- This means that as the length of the spring decreases, the spring constant increases, which is consistent with our previous calculation.

5. **Conclusion**:
- Both the assertion and the reason are correct. The reason also provides a correct explanation for the assertion. Thus, the correct answer is that both A and R are true, and R is the correct explanation for A.

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