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10-1.Thermometry, Thermal Expansion and Calorimetry
hard
A rod of length $10\ meter$ at $0\,^oC$ having expansion coefficient $\alpha = (2x^2 + 1) \times 10^{-6}\,C^{-1}$ where $x$ is the distance from one end of rod. The length of rod at $10\,^oC$ is
A
$11.067$
B
$10.067$
C
$10.0068$
D
$11.0068$
Solution
$\Delta(\mathrm{dx})=\int_{0}^{10}(\alpha \Delta \mathrm{T}) \mathrm{d} \mathrm{x}$
$=\int_{0}^{10}\left(2 x^{2}+1\right) 10 d x \times 10^{-6}=0.006766 \mathrm{m}$
Standard 11
Physics
