A wire has length 8 m, cross-sectional area 2 cm^2, and is made of a material with resistivity 120 ohm metre. What is its resistance in mega ohm?

Introduction / Context:
Electrical resistance depends on the material of a conductor as well as its dimensions. This numerical question tests your ability to use the basic formula that links resistance with resistivity, length, and area. It also checks whether you can correctly convert units such as square centimetre to square metre and then express the final resistance in mega ohm.

Given Data / Assumptions:
- Length of the wire, L = 8 m.- Cross sectional area, A = 2 cm^2.- Resistivity of the material, rho = 120 ohm metre.- We are asked to find resistance in mega ohm (10^6 ohm).

Concept / Approach:
The resistance R of a uniform conductor is given by the formula R = rho * L / A, where rho is resistivity, L is length, and A is cross sectional area. To use this relation, all quantities must be expressed in SI units. That means converting area from square centimetre to square metre. After obtaining R in ohm, we convert it to mega ohm by dividing by 10^6.

Step-by-Step Solution:
1. Convert the area into square metre. Since 1 cm = 10^-2 m, we have 1 cm^2 = 10^-4 m^2.2. Therefore, A = 2 cm^2 = 2 * 10^-4 m^2.3. Use the formula R = rho * L / A.4. Substitute the values: R = 120 * 8 / (2 * 10^-4).5. First calculate the numerator: 120 * 8 = 960.6. Denominator is 2 * 10^-4, so 960 / (2 * 10^-4) = (960 / 2) * 10^4 = 480 * 10^4 ohm.7. 480 * 10^4 ohm = 4.8 * 10^6 ohm.8. Since 1 mega ohm = 10^6 ohm, R = 4.8 mega ohm.

Verification / Alternative check:
As a quick check, note that a relatively long wire with small cross sectional area and fairly high resistivity should give a resistance of the order of mega ohm, not just a few ohm. The calculation yields 4.8 * 10^6 ohm, which matches this expectation. Also, you can recheck the unit conversion: doubling the area would halve the resistance, and lowering resistivity would similarly reduce it, which fits the formula R = rho * L / A.

Why Other Options Are Wrong:
- 1920: This could come from mistakes in handling powers of ten or ignoring the centimetre to metre conversion, leading to an incorrect value.- 2.4: This is half of the correct 4.8 and may result from missing a factor of 2 in the denominator or misapplying the formula.- 960: This corresponds to the intermediate value before properly dividing by 2 * 10^-4 and is not expressed in mega ohm. It shows incomplete calculation.

Common Pitfalls:
The most common errors come from not converting square centimetre to square metre correctly or from mishandling scientific notation. Students may treat 2 cm^2 as 2 * 10^-2 m^2 instead of 2 * 10^-4 m^2, giving a resistance smaller by a factor of 100. Always square the conversion factor when converting area units and carefully track powers of ten during calculations.

Final Answer:
The resistance of the wire is 4.8 mega ohm.