JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Heat & Thermodynamics

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at

3 0^{\circ} C

. The coefficient of linear expansion of aluminium and steel are

24 \times 1 0^{- 6} /^{\circ} C

and

1.2 \times 1 0^{- 5} /^{\circ} C

, respectively. The length of this composite rod when its temperature is raised to

10 0^{\circ} C

, is ______ cm.

(A)120.20
(B)120.15✓ Correct
(C)120.03
(D)120.06

Answer: (B)

Solution

Each rod is

60 cm

long and the two expand independently over

Δ T = 100 - 30 = 70^{\circ} C

. The total length is

60 (1 + α_{A l} Δ T) + 60 (1 + α_{s t} Δ T) = 120 + 60 \times 70 \times (24 + 12) \times 1 0^{- 6} = 120 + 0.1512 = 120.15 cm

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Single correct option

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