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PART - 2 CH - 10 Thermal Properties of Matter — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 10 Thermal Properties of Matter2 Marks
Question
Find out when a 50 m long steel rod of 10 $c m ^2$ cross-section is heated from $0^{\circ} C$ to $50^{\circ} C$ (i) increase in length of rod (ii) if both the ends of the rod are connected to rigid supports, then the force produced in it will know thermal stress. (Given $\alpha=1.2 \times 10^{-5}{ }^{\circ} C ^{-1}$ and $\left.Y =9.6 \times 10^7 N / m ^2\right)$
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Answer

According to question
$\begin{aligned}L_0 & =50 m \\A_0 & =10 cm^2=10 \times 10^{-4} m^2\end{aligned}$
$\begin{aligned}\Delta T & =50^{\circ} C \\\alpha & =1.2 \times 10^{-5}{ }^{\circ} C^{-1} \\Y & =9.6 \times 10^7 Nm^{-2}\end{aligned}$
(i) We know that change in length
$\begin{aligned}\Delta L & =\alpha L_0 \Delta T \\& =1.2 \times 10^{-5} \times 50 \times 50 \\& =12\times 25 \times 10^{-4} \\& =300 \times 10^{-4}=0.03 m\end{aligned}$
(ii) Thermal stress produced in rod
$\begin{array}{l}=Y \alpha \Delta T \\=9.6 \times 10^7 \times 1.2 \times 10^{-5} \times 50 \\=9.6 \times 1.2 \times 50 \times 10^2 \\=5.76 \times 10^4 N / m^2\end{array}$

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