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A rod of circular cross section has a length ‘l’ and radiu ‘r’. It is subjected to a tensile force and the total elastic potential energy stored in the rod is U. If another rod of length 2l and radius 2r is subjected to same tensile force, Then elastic potential energy stored in the rod will be

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a

2 U

b

U4

c

3U4

d

U2

answer is D.

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Detailed Solution

For a rod of length ‘l’ and radius ‘r’, stress σ=Fπr2 ∴u= Energy density =σ22y=F22π2r4y ∴ Energy stored, U=πr2l×u=F2∣2π r2ySuppose total elastic potential energy stored in thesecond rod be U'.∴U′U=l′l×r2r′2=2ll×r2(2r)2=12 ∴U′=U2

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A rod of circular cross section has a length ‘l’ and radiu ‘r’. It is subjected to a tensile force and the total elastic potential energy stored in the rod is U. If another rod of length 2l and radius 2r is subjected to same tensile force, Then elastic potential energy stored in the rod will be