If the ratio of lengths, radii and Young’s moduli of steel and brass wires in the figure are a, b and c respectively, then the corresponding ratio of increase in their lengths is :-
Options

Question

If the ratio of lengths, radii and Young’s moduli of steel and brass wires in the figure are a, b and c respectively, then the corresponding ratio of increase in their lengths is :-

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 B: 3a/(2b²c). Therefore the correct answer is B.