Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:

 Energy density =du/dv, where

u is Energy

v is volume

⇒ du/dv = F2/2A2y (stress = F/A)

⇒ du/dv ∝ 1/A2

⇒ du/dv ∝ 1/d4

(∵Area = π/4 × d4)

A2 = (π/4)2 × d4

⇒du/dv/du/dv =(d2/d1)4

⇒ 1/4 =(d2/d1)4

⇒ (d2/d1)4 =4

⇒ d1/d2 = (4)1/4=2

d1/d2 = √2:1