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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
⇒ 1/4 =(d2/d1)4
⇒ (d2/d1)4 =4
⇒ d1/d2 = (4)1/4=2
d1/d2 = √2:1
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