First slide

Elastic Modulie

Question

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 the steel is Y, then the force with which the steel ring is expanded is

Moderate

A

$\frac{A Y r}{(R - r)}$
B

$\frac{Y (R - r)}{r}$
C

$\frac{A Y (R - r)}{R}$
D

$\frac{A Y (R - r)}{r}$

Solution

Change in length of ring = $2 π R - 2 π r$
Longitudinal strain $= \frac{2 π R - 2 π r}{2 π r} = \frac{R - r}{r}$
Young's modulus, $Y = \frac{F / A}{\frac{R - r}{r}}$
$\Rightarrow Y = \frac{F r}{A (R - r)} \Rightarrow F = \frac{Y A (R - r)}{r}$

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