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Q.

Two wires of same material and length but diameter in the ratio 1 : 3 are stretched by the same force. The potential energy per unit volume for the two wires when stretched will be in the ratio:

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a

3 : 1 

b

9: 1 

c

1: 81

d

81 : 1

answer is D.

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Detailed Solution

Δl=FlAY ⇒Δll=FAY

Potential energy per unit volume  =12× Stress × Strain 

u=12×FA×FAY or  u∝1A2 or u∝1d4

∴ u1u2=d2d14=811

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