Thermal Properties of Matter

JEE Main level, single correct, medium

15 of 126

Question 15 of 126

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.

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Answer: (B) 120.15

Total length at 30°C = 120 cm, each rod = 60 cm
αAl=24×10−6\alpha_{Al} = 24 \times 10^{-6}/°C, αSteel=1.2×10−5\alpha_{Steel} = 1.2 \times 10^{-5}/°C
ΔT=100−30=70\Delta T = 100 - 30 = 70°C
ΔLAl=60×24×10−6×70=0.1008\Delta L_{Al} = 60 \times 24 \times 10^{-6} \times 70 = 0.1008 cm
ΔLSteel=60×1.2×10−5×70=0.0504\Delta L_{Steel} = 60 \times 1.2 \times 10^{-5} \times 70 = 0.0504 cm
Total expansion =0.1008+0.0504=0.1512= 0.1008 + 0.0504 = 0.1512 cm
Final length =120+0.1512=120.15= 120 + 0.1512 = 120.15 cm

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