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

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1 : 3 : 5

5 : 3 : 1

1 : 15 : 125

125 : 15 : 1

answer is D.

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Detailed Solution

R = \frac{ρ l}{A} = \frac{ρ l . l}{V} (∵ V = A l)

$R = \frac{ρ l^{2} d}{m} (∵ V = \frac{m}{d})$

$∴ R \propto \frac{l^{2}}{m}$

$\Rightarrow R_{1} : R_{2} : R_{3} = 125 : 15 : 1$

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