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

Step-by-step solution

We know that, Elastic potential energy in a stretched wire aligned U & = 1 2 Young's modulus ( strain )^2 U & = 1 2 F A 1 I F l Y A U & = 1 2 F^2 A^2 1 Y U & 1 r^4 aligned So, aligned U₁ U₂ & = 1 / r₁^4 1 / r₂^4 = ( r₂ r₁ )^4 [ d₁ d₂ = r₁ r₂ = 1 2 ] U₁ U₂ & = ( 2 1 )^2= 16 1 U₁: U₂ & =16: 1 aligned