First slide

Stress and strain

Question

Two wires of the same material have lengths in the ratio 1 : 2 and radii are in the ratio 1 : √2. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

Moderate

A

1 : √2
B

√2 : 1
C

1 : 1
D

1 : 2

Solution

$\begin{array}{l} Y = \frac{F / {πr}^{2}}{e / I} \\ e = \frac{FI}{{πr}^{2} Y} \\ \frac{e_{1}}{e_{2}} = \frac{I_{1}}{I_{2}} \frac{r_{2}^{2}}{r_{1}^{2}} = \frac{1}{2} \frac{2}{1} (here Y and F are same) \end{array}$

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