Elongation of Bar due to Self Weight

Answer: C.  WL/2AE

Elongation of bar due to self weight is computed by WL/2AE ,Where L-Length of the bar E- Young’s modulus of elasticity and W- Total weight.

Solution

Let, A= Cross sectional area of the bar

E = Young’s modulus 

Υ= Density of bar = WLAL

Consider an element of length dx at a distance x from bottom of the bar being elongated due to the force P at a section x-x.

Weight of the portion below x-x = P = Υ×AX

Change in the length of the element dx

δL = PL/AE=(ΥAx)dx/AE

Total change in length

Δ=∫Axdx/AE

     =ΥE∫x.dx

     =Υ/E[x²/2]

     = ΥL²/2E

     = WL²/AL×2E

     = WL/2AE

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