Question

Two wires of the same material and length, having diameters in the ratio $2:1,$ are stretched by the same force. The potential energy per unit volume stored in the two wires will be in the ratio:-

• A. $1:4$
• B. $4:1$
• C. $16:1$
• D. $1:16$

Answer 1

Answer: (D)

$U=\frac{1}{2}\frac{A Y}{L}\left(\Delta L\right)^{2}$
$\frac{U}{2 L}=u=\frac{1}{2}Y\left(\frac{\Delta L}{L}\right)^{2}$
$\frac{u_{1}}{u_{2}}\left(\left[\frac{\left(\Delta L\right)_{1}}{\left(\Delta L\right)_{2}}\right]\right)^{2}=\left(\frac{A_{2}}{ A_{1}}\right)^{2}=\left(\left[\frac{\frac{\pi }{4} \left(d\right)^{2}}{\frac{\pi }{4} \left(2 d\right)^{2}}\right]\right)^{2}=\frac{1}{16}$