Question

A metallic ring of radius 'r', cross sectional area 'A' is fitted into a wooden circular disk of radius 'R' (R > r). If the Young's modulus of the material of the ring is 'Y', the force with which the metal ring expands is :

• A. $\frac{AYR}{r}$
• B. $\frac{AY(R-r)}{r}$
• C. $\frac{Y(R-r)}{Ar}$
• D. $\frac{YR}{Ar}$

Answer 1

The correct option is B $\frac{AY(R-r)}{r}$

$Y=\frac{F/A}{△l/l}$ (standard result)
$F=\frac{Y△lA}{l}$
$=\frac{Y(R-r)A}{r}(\because △l=R-r)$