For the composite rod shown, l₁=l₂=1 m, A=1 m², F=2 N, Y₁=2×10¹¹ N m⁻² and Y₂=3×10¹¹ N m⁻². Find (i) the net elongation in the form x×10⁻¹¹ m and (ii) the equivalent Young's modulus in the form x×10¹¹ N m⁻². Which option gives the correct pair?
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Question

For the composite rod shown, l₁=l₂=1 m, A=1 m², F=2 N, Y₁=2×10¹¹ N m⁻² and Y₂=3×10¹¹ N m⁻². Find (i) the net elongation in the form x×10⁻¹¹ m and (ii) the equivalent Young's modulus in the form x×10¹¹ N m⁻². Which option gives the correct pair?

Options

G1 Physics · Accepted Answer

Use stress σ=F/A, strain ε=ΔL/L and Young's modulus Y=σ/ε. For a uniform segment, ΔL=FL/(AY); for thermal restraint, thermal strain αΔT produces stress YαΔT. Evaluating the given data/statements gives 1.67; 2.4. Therefore the correct answer is A.