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10-1.Thermometry, Thermal Expansion and Calorimetry
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Two rods of different materials having coefficient of linear expansion $\alpha_1$and $\alpha_2$ and Young's modulii $Y_1$ and $Y_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If $\alpha_1:\alpha_2= 2 : 3$, the thermal stress developed in two rods are equal provided $Y_1 : Y_2$ is equal to
A
$2:3$
B
$4:9$
C
$1:1$
D
$3:2$
Solution
$F=y A \propto(\Delta t)=\left(\frac{F}{A}\right)=y \propto \Delta t$
$y \propto=$ const $\Rightarrow y \propto \frac{1}{\alpha}$
$\frac{y_{1}}{y_{2}}=\frac{\alpha_{2}}{\alpha_{1}}$
$\frac{y_{1}}{y_{2}}=\frac{3}{2}$
Standard 11
Physics
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