Two rods of different materials are placed between massive walls. Their areas are A₁ and A₂, lengths L₁ and L₂, coefficients of linear expansion α₁ and α₂, and Young's moduli Y₁ and Y₂. If they are heated by t°C, find the force F with which they act on each other. Which option gives the correct result?
Options

Question

Two rods of different materials are placed between massive walls. Their areas are A₁ and A₂, lengths L₁ and L₂, coefficients of linear expansion α₁ and α₂, and Young's moduli Y₁ and Y₂. If they are heated by t°C, find the force F with which they act on each other. Which option gives the correct result?

Options

G1 Physics · Accepted Answer

Use ΔL=αLΔT, ΔA≈2αAΔT and ΔV≈3αVΔT (or the given cubical coefficient γ). For constrained bodies include the elastic stress needed to cancel free expansion. Evaluating the given data/statements gives F=(α₁L₁+α₂L₂)t / [L₁/(Y₁A₁)+L₂/(Y₂A₂)]. Therefore the correct answer is A.