Que: A tapering bar (diameters of end sections being d1 and d2) and a bar of uniform cross section d have the same length and are subjected to the same axial pull. both the bars will have the same extension if d is equal to (Engg Services-1998)

(a) d1 + d2 / 2
(b)
(c)    
(d)                  
               
Ans: (b)
Explanation: E = Stress / Strain = WL / ΔL A
For a tapering rod,
A = π d1 d2 / 4
ΔL = 4WL / π d1 d2 E
For a uniform cross section with diameter d,
A = π d² / 4
 ΔL = 4WL / π d² E

The bars have the same length l and are subjected to the same axial pull W. Then for the same extension ΔL
4WL / π d1 d2 E = 4WL / π d² E
1/ d1d2 = 1/ d^{2
so d =}