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  • Two wires of same material and length but diameter in the ratio 1:2 are stretched by the same force. The pote

Two wires of same material and length but diameter in the ratio 1:2 are stretched by the same force. The potential energy per unit volume for the two wires when stretched will be in the ratio-

Option: 1

16:1


Option: 2

4:1


Option: 3

2:1


Option: 4

1:1


Answers (1)

best_answer

\Delta l=\frac{F l}{A Y} \Rightarrow \frac{\Delta l}{l}=\frac{F}{A Y}\\\\ \text {Potential energy per unit volume} =\frac{1}{2} \times stress\times strain\\\\ \begin{aligned} & u=\frac{1}{2} \times \frac{F}{A} \times \frac{F}{A Y} \\\\ & u \alpha \frac{1}{A^2} \text { or } u \propto \frac{1}{d^4} \\\\ & \frac{u_1}{u_2}=\left(\frac{d_2}{d_1}\right)^4=\frac{16}{1} \\\\ & u_1: u_2=16: 1 \end{aligned}

Posted by

Pankaj Sanodiya

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