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10-1.Thermometry, Thermal Expansion and Calorimetry
medium
A steel rod of diameter $1\,cm$ is clamped firmly at each end when its temperature is $25\,^oC$ so that it cannot contract on cooling. The tension in the rod at $0\,^oC$ is approximately ......... $N$ $(\alpha = 10^{-5}/\,^oC,\,\,Y = 2 \times 10^{11}\,N/m^2)$
A
$4000$
B
$7000$
C
$7400$
D
$4700$
Solution
Strain $=\frac{\Delta l}{l}=\alpha \Delta \theta$
Stress $=\mathrm{Y} \times$ strain $=\mathrm{Y} \alpha \Delta \theta$
Force or tension $\mathrm{T}=$ stress $\times$ area
$=\mathrm{YA} \propto \Delta \theta$
$=\frac{\pi \mathrm{Y} \alpha \mathrm{d}^{2} \Delta \theta}{4}\left(\mathrm{A}=\frac{\pi \mathrm{d}^{2}}{4}\right)$
or $\quad \mathrm{T}=\frac{\pi \times 2 \times 10^{11} \times 10^{-5} \times 10^{-4} \times 25}{4}$
$=3926 \mathrm{N}=4000 \mathrm{N}$
Standard 11
Physics
