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

Question

Two wires of the same material and same length but diameters in the ratio 1: 2 are stretched by the same force. The potential energy per unit volume of the two wires will be in the ratio (A) 1: 2 (B) 4: 1 (C) 2: 1 (D) 1: 1

Tardigrade Admin · Accepted Answer

U = ( 1/ Z ) ( σ2 / Y ) ⇒ U propto σ2 propto ( 1/ A2 ) ( U1 / U2 ) = ( A22 / A12 ) = ( d22 / d12 ) = (16/ 1)

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

1 : 2

4 : 1

2 : 1

1 : 1

16 : 1

$U = \frac{1}{Z} \frac{σ ^{2}}{Y}$
$\Rightarrow U \propto σ^{2} \propto \frac{1}{A ^{2}}$
$\frac{U _{1}}{U _{2}} = \frac{A _{2}^{2}}{A _{1}^{2}}$
= $\frac{d _{2}^{2}}{d _{1}^{2}} = \frac{16}{1}$