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Four wires made of same material have different lengths and radii, the wire having least resistance in the following

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a

l = 50cm, r = 2mm

b

l = 100cm, r = 1mm

c

l = 100cm, r = 1/2 mm

d

l = 50cm, r = 1/2 mm

answer is A.

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Detailed Solution

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$R \propto \frac{l}{r^{2}} a) \frac{l}{r^{2}} = \frac{5000}{4} = 1250 \begin{array}{l} b) \frac{l}{r^{2}} = \frac{100}{\frac{1}{100}} = 10000 \\ c) \frac{l}{r^{2}} = \frac{100}{\frac{1}{400}} = 40000 \\ d) \frac{l}{r^{2}} = \frac{50}{\frac{1}{400}} = 20000 \end{array}$

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