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Question

# Find out elongation in a rod.Given : Y=2×1011N/m2,ρ=104kg/m3Y=2×1011N/m2,ρ=104kg/m3

A
9mm
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B
10mm
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C
18mm
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D
3mm
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Solution

## The correct option is A 9mmMass of shaded portion m′=m l( l−x) [where m = total mass = ρA l]T=m′ω2[ l−x2+x] ⇒T=m l( l−x)ω2( l+x2) T=mω22 l( l2−x2)m′ω{ l−x2+x}this tension will be maximum at A(mω2 l2) and minimum at 'B' (zero) elongation in element of width 'dx' = TdxAY Total elongationδ=∫TdxAY=∫l0mω2( l2−x2)2 lAYdxδ=mω22 lAY[ l2x−x33]l0=mω2×2 l22 lAY×3=mω2 l23AY=ρA lω2 l23AYδ=ρω2 l33Y=104×(400)×(1.5)33×2×1011=9×10−3=9mm

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