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

Options

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

Explanation

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

### Step 1: Understand the Assertion
The assertion states that when the radius of a circular loop carrying current is doubled, its magnetic moment becomes four times.

### Step 2: Define Magnetic Moment
The magnetic moment (M) of a circular loop is given by the formula:
\[ M = I \times A \]
where \( I \) is the current flowing through the loop and \( A \) is the area of the loop.

### Step 3: Calculate the Area of the Loop
The area \( A \) of a circular loop is given by:
\[ A = \pi r^2 \]
where \( r \) is the radius of the loop.

### Step 4: Calculate the Initial Magnetic Moment
Let the initial radius be \( r \). Then, the initial magnetic moment \( M \) is:
\[ M = I \times A = I \times \pi r^2 \]

### Step 5: Calculate the New Magnetic Moment When Radius is Doubled
If the radius is doubled, the new radius becomes \( 2r \). The new area \( A' \) is:
\[ A' = \pi (2r)^2 = \pi \times 4r^2 = 4\pi r^2 \]
Thus, the new magnetic moment \( M' \) is:
\[ M' = I \times A' = I \times 4\pi r^2 \]

### Step 6: Relate New Magnetic Moment to Initial Magnetic Moment
Now, we can express \( M' \) in terms of \( M \):
\[ M' = 4 \times (I \times \pi r^2) = 4M \]

### Step 7: Conclusion on Assertion
This shows that when the radius is doubled, the magnetic moment indeed becomes four times the original magnetic moment. Therefore, the assertion is correct.

### Step 8: Analyze the Reason
The reason states that magnetic moment depends on the area of the loop. From our calculations, we see that:
\[ M = I \times A \]
This indicates that magnetic moment is directly proportional to the area of the loop, confirming that the reason is also correct.

### Step 9: Determine the Relationship Between Assertion and Reason
While both the assertion and reason are correct, the reason does not specifically explain why the assertion is true. The assertion is about the effect of doubling the radius on magnetic moment, while the reason is a general statement about the dependence of magnetic moment on area.

### Final Conclusion
Both the assertion and reason are correct, but the reason is not the correct explanation of the assertion. Therefore, the correct answer is that both are true, but the reason does not explain the assertion.