Young's moduli of wires A and B are in the ratio $Y_{A}$ : $Y_{B}$ = 1:4 and their cross-sectional areas are in the ratio $A_{A}$ : $A_{B}$ = 1:3. Equal loads are applied and their lengths are equal. The ratio of elongations Δ $L_{A}$ :Δ $L_{B}$ is:
Options

Question

Young's moduli of wires A and B are in the ratio $Y_{A}$ : $Y_{B}$ = 1:4 and their cross-sectional areas are in the ratio $A_{A}$ : $A_{B}$ = 1:3. Equal loads are applied and their lengths are equal. The ratio of elongations Δ $L_{A}$ :Δ $L_{B}$ is:

Options

G1 Physics · Accepted Answer

Elongation of a wire is ΔL = FL/(AY) For equal force F and equal length L, ΔL ∝ 1/(AY) Therefore, ΔL(A)/ΔL(B) = A(B)Y(B) / [A(A)Y(A)] = (3)(4)/(1)(1) = 12 Hence the ratio is 12:1. Option A follows.