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

Asked in JEE Main Online 2013 · Series and parallel wires

• (1) (3c)/(2ab²)
• (2) (2a²c)/b
• (3) (3a)/(2b²c)
• (4) (2ac)/(b²)

Step-by-step solution

Why the other options are wrong

• (1) comes from inverting both the length ratio and the modulus ratio, putting a and c on the wrong sides of the fraction; Δℓ grows with length and falls with Y, so a belongs upstairs and c downstairs.
• (2) comes from using Δℓ∝(L²)/r, which is what you get if the area is written as π r instead of π r² and the length is squared along with it; it also loses the 3/2 tension ratio entirely.
• (4) comes from taking the loads as equal, so the factor (Tₛₜₑₑₗ)/(T_brass)=(3Mg)/(2Mg) never appears, and then also inverting c; the steel wire carries both blocks, the brass wire only the lower one.

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