A metallic ring of radius 'r' and cross sectional area A is fitted into a wooden circular disc 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 :

The force with which the metal ring expands can be calculated as follows:

$\mathrm{F}=\mathrm{YA}\left(\frac{∆l}{l}\right)$

where:

• ΔL is the change in length of the ring due to its expansion
• L is the original length of the ring
• A is the cross-sectional area of the ring
• Y is the Young's modulus of the material of the ring

$\mathrm{F}=\mathrm{YA}\frac{2\mathrm{\pi }(\mathrm{R}-\mathrm{r})}{2\mathrm{\pi r}}$

$\mathrm{F}=\frac{\mathrm{AY}(\mathrm{R}-\mathrm{r})}{2\mathrm{\pi r}}$

Hence the correct answer is $\mathrm{F}=\frac{\mathrm{AY}(\mathrm{R}-\mathrm{r})}{2\mathrm{\pi r}}$