Question

two wires having same length and material are strached by same force . their diameters are in the ratio 1:3 . the ratio of strain energy per unit volume for these wire (smaller to larger diameter ) when strached is​

Answer 1

Answer:

• Strain energy per unit volume U= 1/2×Stress×Strain

From Hooke's law, Stress=Y×Strain

⟹ U= 1/2Y×(Stress)^2

• where Stress= F/A = F/πd^2/4

⟹ U∝ 1/d^4

Given : d s/dl = 1/3

• Thus ratio of strain energy per unit volume  Us/Ul =( dl/ds)^ 4

⟹  Us/Ul

=>( 3/1)^4

=>81

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