Que: Two tapering bars of the same material are subjected to tensile load P. The larger diameter of each of the bar id D. The diameter of the bar A at its small end is D/2 and bar B is D/3. If both the bar are the same length, then what is the ratio of elongation of bar A to bar B. (Engg Services-2006)

(a) 3 : 2
(b) 2 : 3
(c) 4 : 9
(d) 1 : 3

Ans: (b)
Explanation: For a tapering rod,
ΔL = 4WL / π d1 d2 E

ΔL for A bar = 4WL / (π D D/2 E) = 8WL / (π D² E)

ΔL for B bar = 4WL / (π D D/3 E) = 12WL / (π D² E)

So, Ratio of ΔL for A bar to ΔL for B bar = 8 / 12 =2 / 3