Assertion: When radius of circular loop carrying current is doubled, its magnetic moment becomes four times.
Reason: Magnetic moment depends on area of the loop.

Options

A. If both assertion and reason are ture 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 reson are false.

Explanation

To solve the problem, we need to analyze the assertion and the reason provided in the question.

### Step-by-Step Solution:

1. **Understanding Magnetic Moment**:
The magnetic moment \( m \) of a circular loop carrying current \( I \) is given by the formula:
\[ m = I \times A \]
where \( A \) is the area of the loop.

2. **Calculating the Area of the Loop**:
For a circular loop of radius \( r \), the area \( A \) is calculated as:
\[ A = \pi r^2 \]

3. **Substituting Area into the Magnetic Moment Formula**:
Substituting the area into the magnetic moment formula gives:
\[ m = I \times \pi r^2 \]

4. **Doubling the Radius**:
If the radius \( r \) is doubled, the new radius \( r' \) becomes:
\[ r' = 2r \]

5. **Calculating the New Area**:
The new area \( A' \) with the doubled radius is:
\[ A' = \pi (r')^2 = \pi (2r)^2 = \pi \times 4r^2 = 4\pi r^2 \]

6. **Calculating the New Magnetic Moment**:
The new magnetic moment \( m' \) with the new area becomes:
\[ m' = I \times A' = I \times 4\pi r^2 = 4(I \times \pi r^2) = 4m \]
This shows that the new magnetic moment is four times the original magnetic moment.

7. **Conclusion on Assertion**:
The assertion states that when the radius of the circular loop is doubled, its magnetic moment becomes four times. This is true based on our calculations.

8. **Conclusion on Reason**:
The reason states that the magnetic moment depends on the area of the loop. Since we derived that the area is proportional to the square of the radius, this statement is also true.

9. **Final Evaluation**:
Both the assertion and the reason are true, and the reason correctly explains the assertion.

### Final Answer:
- **Assertion**: True
- **Reason**: True
- **Explanation**: The reason is a correct explanation for the assertion.