The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

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length= 200 cm, diameter= 2 mm

length= 300 cm, diameter= 3 mm

length= 50 cm, diameter= 0.5 mm

length= 100 cm, diameter= 1 mm

answer is C.

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Detailed Solution

Young s modulus, Y=FLAΔL=4FLπD2ΔL or ΔL=4FLπD2Ywhere F is the force applied, L is the length, D is the diameter and ΔL is the extension of the wire respectively.As each wire is made up of same material therefore their Young's modulus is same for each wire.For all the four wires, Y, F (= tension) are the same.∴ ΔL∝LD2 In (a) LD2=200 cm0.2cm2=5×103cm−1 In (b) LD2=300 cm0.3cm2=3.3×103cm−1 In (c) LD2=50 cm0.05cm2=20×103cm−1 In (d) LD2=100 cm0.1cm2=10×103cm−1Hence,ΔL is maximum in (c).

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