A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously,…

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 ΔT. The net change in its length is zero. Let l 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:
  1. lAYα ΔT
  2. A Yα ΔT
  3. AYαΔT
  4. l2 Yα ΔT

Solution

Net change in length =0

Thermal expansion. Δl =lα Δt

Y=FAΔll

Δll=FAY

Δl=FlAY

FlAY=l α Δt

F=AY α Δt

Asked in: JEE Main 2017 (08 Apr Online)

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