Question

Two wires of the same material (Young’s modulus \( Y \)) and same length \( L \) but radii \( R \) and \( 2R \) respectively, are joined end to end and a weight \( W \) is suspended from the combination. The elastic potential energy in the system 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. \( \frac{W^2 L}{\pi R^2 Y} \)

Hint:

Elastic potential energy is stored in the stretching of both wires, with energy distributed based on their cross-sectional areas.