JEE MainPhysicsModerateElasticity

Three bars having lengths [IMAGE] and
[IMAGE] and area of cross section A, A/2, 2A are joined
rigidly end toend. The compound rod is subjected to a stretching force
F. It young's modules of the material of eachrod is Y then the increase
in length of the rod is.
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Show answer and solution

\ \Delta l = \Delta l_{1} + \Delta l_{2} + \Delta l_{3}

\frac{F}{\frac{YA}{\mathcal{l}}} + \frac{F}{\frac{YA}{4\mathcal{l}}} + \frac{F}{\frac{2YA}{3\mathcal{l}}} = \frac{F\mathcal{l}}{YA}\left( 1 + 4 + \frac{3}{2} \right) = \frac{13F\mathcal{l}}{2YA}

Source: Grass-G / Ph-27 Physics paper 2 15 Jan.docx

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