Statement 1: When radius of a circular loop carrying current is doubled, its magnetic moment becomes four times.
Statement 2: Magnetic moment depends on the area of the loop.

Options

A. If both statement 1 and statement 2 are ture, statement 2 is the correct explanation of statement 1.
B. If both statement 1 and statement 2 are ture, statement 2 is not the correct explanation of statement 1.
C. If statement 1 is true, statement 2 is false.
D. If statement 1 is false, statement 2 is true.

Explanation

To analyze the given statements about the magnetic moment of a circular loop carrying current, we can follow these steps:

### Step 1: Understand the Definition of Magnetic Moment
The magnetic moment (M) of a current-carrying loop is defined as the product of the current (I) flowing through the loop and the area (A) of the loop. The formula is given by:
\[ M = I \times A \]

### Step 2: Determine the Area of a Circular Loop
For a circular loop with radius \( r \), the area (A) can be calculated using the formula:
\[ A = \pi r^2 \]

### Step 3: Analyze the Effect of Doubling the Radius
If the radius of the loop is doubled (i.e., \( r \) becomes \( 2r \)), the new area \( A' \) becomes:
\[ A' = \pi (2r)^2 = \pi \times 4r^2 = 4\pi r^2 \]
This shows that the area increases by a factor of 4.

### Step 4: Calculate the New Magnetic Moment
Using the new area, the new magnetic moment \( M' \) can be expressed as:
\[ M' = I \times A' = I \times (4\pi r^2) = 4(I \times \pi r^2) = 4M \]
Thus, the magnetic moment becomes four times the original magnetic moment.

### Step 5: Evaluate the Statements
- **Statement 1**: When the radius of a circular loop carrying current is doubled, its magnetic moment becomes four times. This statement is **true**.
- **Statement 2**: Magnetic moment depends on the area of the loop. This statement is also **true**.

### Conclusion
Both statements are correct, and Statement 2 correctly explains Statement 1. Therefore, the correct answer is that both statements are true.