Question

Two wires of the same material (young's modules Y) and same length L but radii $R$ and $2R$ respectively are joined end to end and a weight $W$ is suspended from the combination as shown in the figure. the elastic potential energy in the system in equilibrium is

• A. $\frac{3W^{2}L}{4\pi R^{2}Y}$
• B. $\frac{3W^{2}L}{8\pi R^{2}Y}$
• C. $\frac{5W^{2}L}{8\pi R^{2}Y}$
• D. $\frac{W^{2}L}{\pi R^{2}Y}$

Answer 1

The correct option is C $\frac{5W^{2}L}{8\pi R^{2}Y}$

$W=\frac{1}{2}\times F\times e=\frac{w^{2}L}{2AY}$

$W=\frac{w^{2}L}{2\left(\pi R^2\right)Y}+\frac{w^{2}L}{2\pi (2R{)}^{2}Y}$

= $\frac{5w^{2}L}{8\pi R^{2}Y}$