Q.

A rod of circular cross section has a length ‘l’ and radius ‘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

2U

b

U4

c

3U4

d

U2

answer is D.

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Detailed Solution

(4)For a rod of length ‘l’ and radius ‘r’,stress σ=Fπr2∴   u=Energy  density = σ22γ=F22π2r4γ∴   Energy  stored,  U=πr2l  ×  u=F2l2πr2γSuppose total elastic potential energy stored in the second rod be U'.∴  U'U=l'l ×  r2r'2=2ll ×  r22r2=12∴    U'=U2
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