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Question

In order to quadruple the resistance of a uniform wire, a part of its length was uniformly stretched till the final length of the entire wire was 1.5 times the original length, the part of the wire was fraction equal to
1044273_de985b9a7a1f4a86b32674c31550ee80.png

A
18
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B
16
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C
110
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D
14
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Solution

The correct option is C 18

Let l be the original length of wire and x be its length stretched uniformly such that final length is 1.5 l

Then 4 R=ρ(lx)A+ρ(0.5l+x)A where A=x(0.5l+x) A

4ρlA=ρlxA+ρ(0.5l+x)2xA

or 4l=lx+14l2x+x2x+lxx

or xl=18

1735013_1044273_ans_b787a3af86ac4c94bae767696e02a745.png

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