Two wires A and B having same length and material are stretched by the same force. Their diameters are in the ratio 1: 3 . The ratio of energy density of wire A to that of wire B when stretched, is

Step-by-step solution

Strain energy per unit volume U= 1 2 Stress Strain From Hooke's law, Stress = Y Strain U = 1 2 Y ( Stress )² where Stress = F A = F d ² / 4 U 1 ~d ⁴ Given : d _ s d _ l = 1 3 Thus ratio of strain energy per unit volume U _ s U ₁ = ( d _ l d _ s )⁴ U _ s U ₁ = ( 3 1 )⁴=81