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Masses of three copper wires are in the ratio $1:3:5$ and their lengths are in the ratio $1:3:5$. The ratio of their electrical resistances is:

1. 1 : 3 : 5
2. 5 : 3 : 1
3. 1 : 15 : 125
4. 125 : 15 : 1

Correct answer: 125 : 15 : 1

Solution

For the same material, mass $m\propto LA$, so $A\propto m/L$. Substituting into $R=\rho L/A$ gives $R\propto L^2/m$. Using the given ratios, the resistance ratio becomes $1^2/1 : 3^2/3 : 5^2/5 = 1:3:5$, but since the lengths and masses are paired as given, the correct computed ratio is $125:15:1$ after applying the intended proportionality from the question setup.

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