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Question

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


A
Length=50 cm,diameter=0.5 mm
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B
Length=100 cm,diameter=1 mm
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C
Length=200 cm,diameter=2 mm
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D
Length=300 cm,diameter=3 mm
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Solution

The correct option is B $$Length = 50\ cm, diameter = 0.5\ mm$$
Using Hook'e law       $$Y = \dfrac{F L}{A \Delta L}$$              where  $$A = \dfrac{\pi D^2}{4}$$
$$\implies$$   $$\Delta L  = K \dfrac{L}{D^2}$$              where  $$K = constant$$
For wire A :  $$\dfrac{L}{D^2}  = \dfrac{50 }{(0.05)^2}   =20000$$

For wire B :  $$\dfrac{L}{D^2}  = \dfrac{100 }{(0.1)^2}   =10000$$

For wire C :  $$\dfrac{L}{D^2}  = \dfrac{200 }{(0.2)^2}   =5000$$

For wire D :  $$\dfrac{L}{D^2}  = \dfrac{300 }{(0.3)^2}   =3333.33$$
Thus wire A has the largest extension.

Physics

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