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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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