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Q.

The ratio of diameters of two wires, made of same material is 2:1. The ratio of their lengths is 1:2. On applying the same tensile force to the wires, the ratio of elastic potential energies stored in the wires will be

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a

1:2

b

1:4

c

1:16

d

1:8

answer is D.

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Detailed Solution

stress σ=Fπr2strain energy per unit volume u=σ22Y∴ Total elastic potential energy stored in the wire, U=u×πr2l=F2l2πYr2∴ U1U2=(l1l2)(r2r1)2=(12)(12)2=18

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