A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by Δ T. The net change in its length is zero. Let be the length of the rod, A its area of cross-section,Y its Young’s modulus, and α its coefficient of linear expansion. Then, F is equal to: (a) 2 Y α Δ T (b) A Y α Δ T (c) A Y α Δ T (d) (AY)/(α Δ T)

Answer: (c). Compression must cancel thermal strain: F/AY = αΔ T. So F = AYαΔ T, answer (c).

A compressive force, F is applied at the two ends of a long thin… | JEE Main 2017 (8 Apr, Shift 1)

Q65JEE Main 2017 · 8 APR · SHIFT 1Medium

Thermometry & Thermal Expansion

A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $\Delta$ T. The net change in its length is zero. Let $\ell$ be the length of the rod, A its area of cross-section,Y its Young’s modulus, and $\alpha$ its coefficient of linear expansion. Then, F is equal to:

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Answer: (c)

Compression must cancel thermal strain: $\dfrac{F}{AY} = \alpha\Delta T$ .
So $F = AY\alpha\Delta T$ , answer (c).

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Thermometry & Thermal Expansion question from JEE Main 2017 (8 Apr, Shift 1)

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