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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

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 18Let l be the original length of wire and x be its length stretched uniformly such that final length is 1.5 lThen 4 R=ρ(l−x)A+ρ(0.5l+x)A′ where A′=x(0.5l+x) A∴4ρlA=ρl−xA+ρ(0.5l+x)2xAor 4l=l−x+14l2x+x2x+lxx or xl=18

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