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Physics · Thermal Properties of Matter

JEE Main 2026 — 21 January, Morning Shift — Question 38

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30∘C30^{\circ} \mathrm{C}. The coefficient of linear expansion of aluminium and steel are 24×10−6/∘C24 \times 10^{-6} /{ }^{\circ} \mathrm{C} and 1.2×10−5/∘C1.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}, respectively. The length of this composite rod when its temperature is raised to 100∘C100^{\circ} \mathrm{C}, is ____\_\_\_\_ cm.

  1. Option A:

    120.2

  2. Option B:

    120.15

    Correct
  3. Option C:

    120.03

  4. Option D:

    120.06

Answer: B

Step-by-step solution

ℓfinal =ℓ0(1+αAΔT)+ℓ0(1+αBΔT)\ell_{\text {final }}=\ell_{0}\left(1+\alpha_{\mathrm{A}} \Delta \mathrm{T}\right)+\ell_{0}\left(1+\alpha_{\mathrm{B}} \Delta \mathrm{T}\right)

=ℓ0[2+(αA+αB)ΔT]=60[2+(36×10−6)×70]=60[2+0.0025]=120.15 cm\begin{aligned} & =\ell_{0}\left[2+\left(\alpha_{\mathrm{A}}+\alpha_{\mathrm{B}}\right) \Delta \mathrm{T}\right] & =60\left[2+\left(36 \times 10^{-6}\right) \times 70\right] & =60[2+0.0025] & =120.15 \mathrm{~cm} \end{aligned}

Answer key and solution verified before publishing.

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Exam
JEE Main 2026
Paper
21 January, Morning Shift
Subject
Physics
Chapter
Thermal Properties of Matter
Topic
Thermal Expansion of Solids and its Applications

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