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Question

# A wire of resistance 100 Ω is stretched so that its radius becomes half the initial value. What will be the new resistance of the wire?

A
400 Ω
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B
800 Ω
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C
1200 Ω
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D
1600 Ω
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Solution

## The correct option is D 1600 ΩResistance of the wire is, R=ρlA=ρlAA2=ρV(πr2)2 ∵ ρ and V(volume) are constant ⇒ R∝1r4 ⇒ R′R=(rr′)4 [∵r′=r2] ⇒R′R=⎡⎢ ⎢ ⎢ ⎢⎣r(r2)⎤⎥ ⎥ ⎥ ⎥⎦4=24 R′=16×R R′=16×100=1600 Ω <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (D) is the correct answer.

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