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If 25% part of the length of a wire is stretched by 25%, then the percentage change in the resistance of the wire will be about

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a

7%

b

14%

c

25%

d

62.5%

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detailed solution

Correct option is B

Resistance of the wire after stretching,
$\begin{array}{l} R^{''} = R_{1} + R_{2} = \frac{3 R}{4} + (1.25)^{2} \frac{R}{4} \\ = \frac{3 R}{4} + \frac{25}{16} \frac{R}{4} = \frac{73 R}{64} \\ ∴ % change = \frac{R^{''} - R^{'}}{R^{'}} \times 100 = \frac{\frac{73 R}{64} - R}{R} \times 100 \\ = \frac{900}{64} = 14.06 \end{array}$

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