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Thermal stress or force in a rod that is not allowed to expand or contract

This type of question, asked 5 times: 2021 Paper 13, 2021 Paper 24, 31 Jan 2023, 8 Apr 2023, 24 Jan 2026 S1. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 13

    16
    A section of a railway track is clamped between two nails. In summers it gets heated up and as a result, some elastic energy is stored in it. If ΔT=10∘C,α=10−6 ∘C−1=\Delta T=10^{\circ}C, \alpha = 10^{-6}\ ^{\circ}C^{- 1} = coefficient of linear expansion, Y=1011Nm−2=Y=10^{11}Nm^{- 2}= Young's modulus, A=0.01 m2=A= 0.01{\text{ }m}^{2}= Area of cross section. Find the energy stored per unit length in the railway track.

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  2. Question 2

    2021 Paper 24

    27
    A steel rod with y=2.0×1011Nm−2y = 2.0 \times10^{11}Nm^{- 2} and α=10−5 ∘C−1\alpha=10^{- 5}\ ^{\circ}C^{- 1} of length 4 m4\text{ }m and area of cross-section 10 cm210{\text{ }cm}^{2} is heated from 0∘C0^{\circ}C to 400∘C400^{\circ}C without being allowed to extend. The tension produced in the rod is x×105 Nx \times10^{5}\text{ }N where the value of xx is

  3. Question 3

    31 Jan 2023

    30
    A thin rod having a length of 1 m1\text{ }m and area of cross-section 3×10−6 m23 \times10^{- 6}{\text{ }m}^{2} is suspended vertically from one end. The rod is cooled from 210∘C210^{\circ}C to 160∘C160^{\circ}C. After cooling, a mass MM is attached at the lower end of the rod such that the length of rod again becomes 1 m1\text{ }m. Young's modulus and coefficient of linear expansion of the rod are 2×1011 N m−22 \times10^{11}\text{ }N{\text{ }m}^{- 2} and 2×10−5 K−12 \times10^{- 5}{\text{ }K}^{- 1}, respectively. The value of MM is__ kgkg. (Take g=10 m s−2g = 10\text{ }m{\text{ }s}^{- 2} )

  4. Question 4

    8 Apr 2023

    115
    A steel rod of length 1 m1\text{ }m and cross-sectional area 10−4 m210^{- 4}{\text{ }m}^{2} is heated from 0∘C0^{\circ}C to 200∘C200^{\circ}C without being allowed to extend or bend. The compressive tension produced in the rod is___ ×104 N\times10^{4}\text{ }N. (Given Young's modulus of steel =2×1011Nm−2= 2 \times10^{11}Nm^{- 2}, coefficient of linear expansion =10−5 K−1=10^{- 5}{\text{ }K}^{- 1}.

  5. Question 5

    24 Jan 2026 S1

    14
    A brass wire of length 2 m and radius 1 mm at 27∘C27^{\circ}C is held taut between two rigid supports. Initially it was cooled to a temperature of −43∘C-43^{\circ}C creating a tension T in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to 1.4 T , is ____\_\_\_\_  ∘C\ ^{\circ}C

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