Find the resistance, in megaohms (MΩ), of a wire of length 20 m and cross-sectional area 1 cm² made of a material whose resistivity is 200 Ω·m.

Introduction / Context:
This question checks your understanding of the relationship between resistance, resistivity, length and cross sectional area of a conductor. It also tests your ability to handle unit conversions, particularly from square centimetres to square metres and from ohms to megaohms. The goal is to compute the resistance of a wire using the standard formula R = rho * l / A.

Given Data / Assumptions:

• Resistivity of the material, rho = 200 Ω·m.
• Length of the wire, l = 20 m.
• Cross sectional area, A = 1 cm².
• We are asked for resistance in megaohms (MΩ), where 1 MΩ = 10^6 Ω.
• The wire is uniform, with constant cross sectional area and resistivity.

Concept / Approach:
The resistance R of a uniform conductor is given by R = rho * l / A. To use this formula consistently in SI units, resistivity should be in Ω·m, length in metres and area in square metres. Therefore, we must convert 1 cm² to m². Once we compute R in ohms, we then convert that value into megaohms by dividing by 10^6.

Step-by-Step Solution:
Step 1: Convert the area from cm² to m². Since 1 cm = 10^-2 m, 1 cm² = (10^-2 m)² = 10^-4 m². So A = 1 * 10^-4 m². Step 2: Write the resistance formula: R = rho * l / A. Step 3: Substitute the values: R = 200 Ω·m * 20 m / (1 * 10^-4 m²). Step 4: Multiply the numerator: 200 * 20 = 4000 Ω·m². Step 5: Divide by 10^-4 m²: R = 4000 / 10^-4 Ω = 4000 * 10^4 Ω = 4 * 10^7 Ω. Step 6: Convert ohms to megaohms: R = 4 * 10^7 Ω / 10^6 = 40 MΩ.

Verification / Alternative check:
You can check the order of magnitude: a long wire (20 m) of relatively high resistivity (200 Ω·m) and very small cross sectional area (1 cm² is 10^-4 m²) should have a large resistance. The formula R = rho * l / A shows that if the area is tiny and resistivity and length are large, R should be very large, in the tens of megaohms range. Our answer 40 MΩ is consistent with this expectation and matches option 40.

Why Other Options Are Wrong:
4000: This would correspond to 4000 MΩ if read directly or 4000 Ω if interpreted wrongly, both inconsistent with the calculation based on correct units.

80 and 2000: These values do not match the computed 40 MΩ and likely result from incorrect handling of the 10^-4 factor or from forgetting to convert to megaohms.

Common Pitfalls:
A frequent mistake is to treat 1 cm² as 10^-2 m² instead of 10^-4 m², forgetting that the square applies to the whole conversion factor. Another common error is to forget the final conversion to megaohms and leave the answer in plain ohms, or to incorrectly multiply instead of divide by 10^6. Always keep track of units at each step and remember that 1 MΩ = 10^6 Ω.

Final Answer:
The resistance of the wire is 40 megaohms (40 MΩ).