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A steel ring of radius r and cross-sectional area A is fitted on to a wooden disc of radius R (R>r). If Young's modulus of steel is Y, then the force with which the steel ring is expanded is:-
Option: 1
$A Y \frac{R}{r}$

Option: 2
$A Y \frac{R-r}{r}$

Option: 3
$\frac{Y}{A}\left(\frac{R-r}{r}\right)$

Option: 4
$\frac{Yr}{A R}$

Answers (1)

best_answer

$Strain \:\: e=\frac{\Delta r}{r} = \frac{R-r}{r}$

$Stress\: f= eY=\left ( \frac{R-r}{r} \right )Y$

$force \: needed\: F=fa =(\frac{R-r}{r})YA$

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Rishi

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