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

Question

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

Infinity Learn · Accepted Answer

$$(4)For$$ a rod of length ‘l’ and radius ‘r’,stress σ$$=F$$$$π$$$$r2$$∴   $$u=Energy$$  density $$=$$ σ$$22$$γ$$=F22$$$$π$$$$2r4$$γ∴   Energy  stored,  $$U=$$π$$r2l$$  ×  $$u=F2l2$$$$π$$$$r2$$γSuppose 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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