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A piece of copper having mass m is drawn into a wire and its resistance is found to be $10 Ω$ . When a piece of copper of mass 4 m is drawn into a wire of same length, its resistance will be

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$40 Ω$

$2.5 Ω$

$20 Ω$

$5 Ω$

answer is B.

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Detailed Solution

If d is the density of copper, then

$m = A l d \Rightarrow A = \frac{m}{l d}$

$∴ R = ρ . \frac{l}{A} = ρ . \frac{l}{m / l d} = \frac{ρ d l^{2}}{m} \Rightarrow R \propto \frac{1}{m}$

$∴ \frac{R'}{R} = \frac{m}{4 m} \Rightarrow R' = \frac{R}{4} = \frac{10}{4} Ω = 2.5 Ω$

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