First slide

Stress and strain

Question

Two wires A and B are of same materials. Their lengths are in the ratio I : 2 and diameters are in the ratio 2 : I when stretched by force $F_{A} and F_{B}$ respectively they get equal increase in their lengths. Then the ratio $\frac{F_{A}}{F_{B}}$ should be

Moderate

A

1 : 2
B

1 : 1
C

2 : 1
D

8 : 1

Solution

$F = Y \times A \times \frac{l}{L} \Rightarrow F \propto \frac{r^{2}}{L} (Y and l are constant)$
$\frac{F_{A}}{F_{B}} = {(\frac{r_{A}}{r_{B}})}^{2} \times (\frac{L_{B}}{L_{A}}) = {(\frac{2}{1})}^{2} \times (\frac{2}{1}) = \frac{8}{1}$

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