The electrical resistance of a column of 0.04M NaOH solution of diameter 1.2 cm and length 50cm is `5.55xx10^(3)ohm`, the resistivity of the column would be

Options

A. 125.47ohm cm
B. 120.47ohmcm
C. 102,47 ohm cm
D. 12.547ohm cm.

Explanation

To find the resistivity of the NaOH solution, we can use the formula for electrical resistance:

\[ R = \frac{\rho L}{A} \]

Where:
- \( R \) is the resistance (in ohms)
- \( \rho \) is the resistivity (in ohm-meter)
- \( L \) is the length of the conductor (in meters)
- \( A \) is the cross-sectional area (in square meters)

### Step-by-Step Solution:

1. **Convert the diameter to radius**:
- Given diameter = 1.2 cm
- Radius \( r = \frac{diameter}{2} = \frac{1.2 \, \text{cm}}{2} = 0.6 \, \text{cm} \)

**Hint**: Remember that the radius is half of the diameter.

2. **Convert radius to meters**:
- \( r = 0.6 \, \text{cm} = 0.006 \, \text{m} \) (since 1 cm = 0.01 m)

**Hint**: Always convert units to SI units for consistency.

3. **Calculate the cross-sectional area \( A \)**:
- Use the formula for the area of a circle:
\[ A = \pi r^2 \]
- \( A = \pi (0.006 \, \text{m})^2 \)
- \( A \approx 3.14 \times (0.006)^2 = 3.14 \times 0.000036 = 0.00011304 \, \text{m}^2 \)

**Hint**: Ensure you square the radius correctly and multiply by \( \pi \).

4. **Convert the length \( L \) to meters**:
- Given length = 50 cm
- \( L = 50 \, \text{cm} = 0.5 \, \text{m} \)

**Hint**: Again, convert all measurements to SI units.

5. **Substitute values into the resistance formula to find resistivity \( \rho \)**:
- Given \( R = 5.55 \times 10^3 \, \Omega \)
- Rearranging the formula gives:
\[ \rho = \frac{R \cdot A}{L} \]
- Substitute the known values:
\[ \rho = \frac{(5.55 \times 10^3 \, \Omega) \cdot (0.00011304 \, \text{m}^2)}{0.5 \, \text{m}} \]

6. **Calculate \( \rho \)**:
- \( \rho = \frac{5.55 \times 10^3 \cdot 0.00011304}{0.5} \)
- \( \rho = \frac{0.628 \, \Omega \cdot \text{m}^2}{0.5} \)
- \( \rho = 1.256 \, \Omega \cdot \text{m} \)

**Hint**: Make sure to perform the multiplication and division carefully.

### Final Answer:
The resistivity of the NaOH solution is approximately \( 1.256 \, \Omega \cdot \text{m} \).