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Longitudinal Stress

Stress genera...

Question

Stress generated in a wire when force $F_{1}$ acts on it as shown in the figure, is $T$ . Initial cross sectional area of the wire is $A_{1}$ . When force $F_{2}$ replaces $F_{1}$ , cross-sectional area becomes $A_{2}$ . Find $(\frac{A_{2}}{A_{1}})$ if $F_{2} = 6 N$ .
[Consider stress generated in the wire to be the same]

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Solution

The correct option is A $3$
Given,
Stress generated in the wire is same in both cases.
$Stress generated when F_{1} acts = Stress generated when F_{2} acts$

$\Rightarrow \frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}$
$\Rightarrow \frac{2}{A_{1}} = \frac{6}{A_{2}}$
$\Rightarrow \frac{A_{2}}{A_{1}} = \frac{6}{2} = 3$

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