Two rods of different materials, having the same length and the same cross-sectional…

Physics · JEE Main · NTA Exams — Properties of Solids and Liquids

Two rods of different materials, having the same length and the same cross-sectional area, coefficient of linear expansion \(\mathbf{I}_{1}\) and \(x_{2}\) and Youngs modulus Y1 and Y2, respectively. They are fixed between the two rigid walls as shown in the figure. There is no initial stress in the rod. When its temperature is increased by \(\Delta \mathrm{T}\), the stress in the rod will be

\(\begin{array}{|ll|} \hline \boldsymbol{\alpha}_{\mathbf{1}} & \boldsymbol{a}_{\mathbf{2}} \\ \hline \hline \end{array}\)

  1. \(\frac{\left[\mathbf{a}_{1}-\mathbf{a}_{2}\right] \Delta T}{\frac{1}{Y_{2}}+\frac{1}{Y_{1}}}\)
  2. \(\frac{\left[\mathbf{a}_{1}-\mathbf{a}_{2}\right] \Delta T}{\frac{1}{Y_{2}}-\frac{1}{Y_{1}}}\)
  3. \(\frac{\left[\mathbf{a}_{1}+\mathbf{a}_{2}\right] \Delta T}{\frac{1}{Y_{2}}-\frac{1}{Y_{1}}}\)
  4. \(\frac{\left[\mathbf{a}_{1}+\mathbf{a}_{2}\right] \Delta T}{\frac{1}{Y_{2}}+\frac{1}{Y_{1}}}\)

Answer

(A) [ a _ 1 - a _ 2 ] T 1 Y_ 2 + 1 Y_ 1

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