Question

A metallic ring of radius $2cm$ and cross sectional area $4c{m}^2$ is fitted into a wooden circular disc of radius $4cm$.If the Young's module of the material of the ring is $2\times {10}^{11}N/m^2$, the metal ring expand is:

• A. $2\times {10}^{7}N$
• B. $8\times {10}^{7}N$
• C. $4\times {10}^{7}N$
• D. $6\times {10}^{7}N$

Answer 1

Answer: (B)

$8\times {10}^{7}N$

$\begin{array}{c}\text{Given, metal ring of radius}=2cm\\ \text{cross - sectional area}=4{cm}^2\\ \text{Young's modulus of ring}=2\times {10}^{11}\frac{N}{m^{\prime }}\end{array}$

$\begin{array}{c}{l}_i=2\pi r\\ l_{+}=2\pi R\\ \frac{\Delta l_i}{l_i}=\frac{R-r}{\gamma }=\frac{4-2}{2}=1\\ \therefore \text{Stress}=Y\left(\frac{\Delta l}{l}\right)=2\times {10}^{\prime \prime }\\ \therefore \text{Force}=2\times {10}^{\prime \prime }\times 4\times {10}^{-4}\\ =8\times {10}^{7}N\end{array}$