A metallic bar of Young's modulus, $0.5 imes 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ and coefficient

Question

A metallic bar of Young's modulus, $0.5 	imes 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ and coefficient of linear thermal expansion $10^{-5}{ }^{\circ} \mathrm{C}^{-1}$, length 1 m and area of cross-section $10^{-3} \mathrm{~m}^2$ is heated from $0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ without expansion or bending. The compressive force developed in it is

Professor PC Thomas Classes · Answer

$\begin{aligned} & 	ext { (b) : } Y=0.5 	imes 10^{11} \mathrm{~N} / \mathrm{m}^2, \alpha=10^{-5} /{ }^{\circ} \mathrm{C} \ & l=1 \mathrm{~m}, A=10^{-3} \mathrm{~m}^2, \Delta T=100^{\circ} \mathrm{C} \ & F=Y A \alpha \Delta T \ & F=0.5 	imes 10^{11} 	imes 10^{-3} 	imes 10^{-5} 	imes 100 \ & F=50 	imes 10^3 \mathrm{~N}\end{aligned}$