Que: A solid uniform bar of diameter d and length l is hanging vertically from its free end. The elongation of the bar due to self weight is (Engg Services-2005)

(a) Proportional to l and inversely Proportional to to d²
(b) Proportional to l² and inversely proportional to d²
(c) Proportional to l but independent of d
(d) Proportional to l² but independent of d

Ans: (a)
Explanation: Extension due to self weight (W) is
Here E = Modulus of elasticity
d = Diameter of rod
L = Length of rod
ΔL = Elongation

From equation of modulus of elasticity of self weighted rod = E = (W x L) / 2(π/4 d² x ΔL)
ΔL = (W x L) / 2(π/4 d² x E)
From above equation concluded that Elongation (ΔL) are directly Proportional to l and inversely Proportional to to d²