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A rod of length L at room temperature and uniform area of cross-section A is made of a metal having coefficient of linear expansion α °C⁻¹. It is observed that an external compressive force F, applied on each of its ends, prevents any change in the length of the rod when its temperature rises by Δ T. Young's modulus Y for this metal is

Asked in JEE Main 9th Jan 1st Shift 2019 · Thermal stress and strain

• (1) (2F)/(AαΔ T)
• (2) F/(AαΔ T)
• (3) F/(2AαΔ T)
• (4) F/(Aα(Δ T-273))

Step-by-step solution

Why the other options are wrong

• (1) comes from doubles the force because it is applied at each of the two ends. A rod squeezed by F at both ends carries a stress F/A at every cross-section, not (2F)/A — cut it anywhere and only one F acts on the piece you keep.
• (3) comes from shares the force between the two ends, halving it. The same cut argument applies: the internal force at any section is the full F.
• (4) comes from converts a temperature difference to kelvin by subtracting 273. A difference is numerically the same in °C and in K; the 273 shifts a reading, not an interval.

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