Correct Answer: Option C

Explanation

To calculate the length of the wire, we use the formula for resistance:

\(R = \frac{\rho \cdot L}{A}\)

Where:
- \( R \) is the resistance (21 Ω),
- \( \rho \) is the resistivity (\( 1.1 \times 10^{-8} \, \Omega \, m \)),
- \( L \) is the length of the wire,
- \( A \) is the cross-sectional area (\( 2\pi \times 10^{-8} \, m^2 \)).

Rearranging the formula to solve for length \( L \): \(L = \frac{R \cdot A}{\rho}\)

Substituting the known values, we first calculate the area \( A \):

\(A = 2\pi \times 10^{-8} \, m^2 = 2 \times \frac{22}{7} \times 10^{-8} \approx 8.0 \times 10^{-8} \, m^2\)

Now substitute into the length formula: \(L = \frac{21 \, \Omega \cdot 8.0 \times 10^{-8} \, m^2}{1.1 \times 10^{-8} \, \Omega \, m}\)

Calculating:

\(L = \frac{21 \cdot 8.0}{1.1}\)m

\(L = \frac{168}{1.1} \, m \approx 120\)m

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