First slide

Stress and strain

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?

Easy

A

Length = 50 cm, diameter = 0.5 mm
B

Length = 100 cm, diameter = 1 mm
C

Length = 200 cm, diameter = 2 mm
D

Length = 300 cm, diameter = 3 mm

Solution

$Δ L = \frac{F L}{A Y} or Δ L \propto \frac{L}{d^{2}}$ $(∵ A = \frac{π d^{2}}{4})$
Therefore, $Δ L$ will be maximum for that wire for which $\frac{L}{d^{2}}$ is maximum. Here by checking options, we get option (a) has maximum extension.

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