If a wire of resistance `1Omega` is stretched to double its length, then the resistnance will become

Options

A. `1/2 Omega`
B. `2 Omega `
C. `1/4 Omega`
D. `4 Omega`

Explanation

To solve the problem of how the resistance of a wire changes when it is stretched to double its length, we can follow these steps:

### Step 1: Understand the formula for resistance
The resistance \( R \) of a wire is given by the formula:
\[ R = \frac{\rho L}{A} \]
where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the wire,
- \( A \) is the cross-sectional area of the wire.

### Step 2: Identify the initial conditions
We are given:
- Initial resistance \( R = 1 \, \Omega \)
- Initial length \( L \)
- Initial cross-sectional area \( A \)

### Step 3: Analyze the change when the wire is stretched
When the wire is stretched to double its length, the new length \( L' \) becomes:
\[ L' = 2L \]

### Step 4: Determine the change in cross-sectional area
Since the volume of the wire remains constant during stretching, we can express the volume as:
\[ V = A \times L \]
Initially, the volume is:
\[ V = A \times L \]
After stretching, the new volume is:
\[ V' = A' \times L' = A' \times 2L \]
Setting the two volumes equal gives:
\[ A \times L = A' \times 2L \]
From this, we can solve for the new cross-sectional area \( A' \):
\[ A' = \frac{A}{2} \]

### Step 5: Substitute the new values into the resistance formula
Now we can find the new resistance \( R' \) using the new length and new cross-sectional area:
\[ R' = \frac{\rho L'}{A'} = \frac{\rho (2L)}{A/2} \]
This simplifies to:
\[ R' = \frac{2\rho L}{A/2} = \frac{2\rho L \cdot 2}{A} = \frac{4\rho L}{A} \]

### Step 6: Relate the new resistance to the initial resistance
From the initial resistance formula, we know:
\[ R = \frac{\rho L}{A} \]
Thus, we can express \( R' \) in terms of \( R \):
\[ R' = 4 \cdot \frac{\rho L}{A} = 4R \]
Since \( R = 1 \, \Omega \):
\[ R' = 4 \times 1 \, \Omega = 4 \, \Omega \]

### Conclusion
The new resistance of the wire after it is stretched to double its length is:
\[ \boxed{4 \, \Omega} \]