Thermal Properties of Matter

JEE Main level, single correct, medium

41 of 126

Question 41 of 126

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

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Answer: (B) AYαΔTAY\alpha \Delta T

Net change in length =0=0

Thermal expansion. Δl\Delta l=lαΔt=l\alpha \Delta t

Y=FAΔllY=\dfrac{\dfrac{F}{A}}{\dfrac{\Delta l}{l}}

Δll=FAY\dfrac{\Delta l}{l}=\dfrac{F}{AY}

Δl=FlAY\Delta l=\dfrac{Fl}{AY}

FlAY=lαΔt\dfrac{Fl}{AY}=l\alpha \Delta t

F=AYαΔtF=AY\alpha \Delta t

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