First slide

Elastic Modulie

Question

The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum when the same tension is applied

Moderate

A

Length 100 cm, Diameter I mm
B

Length 200 cm, Diameter 2 mm
C

Length 300 cm, Diameter 3 mm
D

Length 50 cm, Diameter 0.5 mm

Solution

$Y = \frac{F}{A} \frac{L}{A} \Rightarrow l \propto \frac{L}{A} \propto \frac{L}{{πd}^{2}}$
$∴ l \propto \frac{L}{d^{2}}$ [As F and Y are constant]
The ratio of $\frac{L}{d^{2}}$ is maximum for case (4)

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