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

A metallic bar of Young's modulus, $0.5 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ 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 :
  1. $50 \times 10^3 \mathrm{~N}$
  2. $100 \times 10^3 \mathrm{~N}$
  3. $2 \times 10^3 \mathrm{~N}$
  4. $5 \times 10^3 \mathrm{~N}$

Solution

$\begin{aligned} & \text { Thermal strain }=\text { Longitudinal strain }=\alpha \Delta T \\ & \Rightarrow \quad \text { Longitudinal strain, } \delta=10^{-5} \times 10^2=10^{-3} \\ & \Rightarrow \quad \text { Compressive stress }=\delta \times \text { Young's Modulus } \\ & =10^{-3} \times 0.5 \times 10^{11} \\ & =0.5 \times 10^8 \\ & \Rightarrow \quad \text { Compressive force }=0.5 \times 10^8 \times 10^{-3}=0.5 \times 10^5 \\ & \quad=5 \times 10^4 \times \frac{10}{10} \\ & =50 \times 10^3 \mathrm{~N}\end{aligned}$

Asked in: NEET 2024

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