Question

A steel ring of radius $r$ and cross sectional area $A$ is fitted onto a wooden disc of radius $R(R>r)$. If the Young's modulus of steel is $Y$, then the force with which the steel ring is expanded is

• A. $AY\left(R/r\right)$
• B. $AY(R-r)/r$
• C. $\left(Y/A\right)\left[\right(R-r\left)/r\right]$
• D. $Yr/AR$

Answer 1

The correct option is B $AY(R-r)/r$

Let $T$ be the tension in the ring, then
$Y=\frac{T.2\pi r}{A.2\pi (R-r)}=\frac{Tr}{A(R-r)}$
$\therefore T=\frac{YA(R-r)}{r}$