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Question

# Two wires A and B are made of same material. The wire A has a length l and diameter r while the wire B has length 2l and diameter 2r. If the two wires are stretched by the same force, the elongation in A divided by elongation in B is

A

1/8

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B

1/4

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C

4

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D

8

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Solution

## The correct option is A 1/8 Let the magnitude of constant force be F. For wire A: Stress=FA=F(πr24) Strain developed =ΔLAl young's modulus,Y=4Flπr2ΔLA for wire B Stress=FA=F(πr216)=16Fπr2 Strain=ΔLg2l Y=2×16Flπr2ΔLB=32Flπr2ΔLB Equating both [as both are of same material} ⇒4Flπr2ΔLA=32Flπr2ΔLB ⇒ΔLAΔLB=18

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