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Topic: Heat, temperature and thermal expansion· Properties of Solids and Liquids

A metallic bar of Young's modulus, 0.5×10^11 N m^-2 and coefficient of linear thermal expansion 10^-5 ^°C^-1, length 1 m and area of cross-section 10^-3 m^2 is heated from 0^°C to 100^°C without expansion or bending. The compressive force developed i…

A metallic bar of Young's modulus, \(0.5\times10^{11}\) N m\(^{-2}\) and coefficient of linear thermal expansion \(10^{-5}\,{}^\circ\)C\(^{-1}\), length 1 m and area of cross-section \(10^{-3}\) m\(^2\) is heated from \(0^\circ\)C to \(100^\circ\)C without expansion or bending. The compressive force developed in it is:

1. \(2\times10^3\) N

2. \(5\times10^3\) N

3. \(50\times10^3\) N

4. \(100\times10^3\) N

1 answer

Best answer

Answer: 3. \(50\times10^3\) N

Key idea: If the bar is not allowed to expand, the thermal strain \(\alpha\Delta T\) is cancelled by a compressive strain, so a stress \(Y\alpha\Delta T\) develops.

\(F=YA\alpha\Delta T=0.5\times10^{11}\times10^{-3}\times10^{-5}\times100=5\times10^{4}\) N \(=50\times10^3\) N.

Option 3.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report
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