First slide

Stress and strain

Question

A thin rod AB of length l, cross sectional area A and young's modulus Y is acted upon by three forces as shown in figure. Then total elongation produced in the rod is [C is the mid point of the rod]

Difficult

A

$\frac{3 Fl}{AY}$
B

$3 Fl / 2 AY$
C

$4 Fl / AY$
D

$\frac{5 Fl}{2 AY}$

Solution

Segment AC of the rod is under a tensile force of F and segment BC is under a tensile force of 2F.
$∴ δ = δ_{AC} + δ_{BC} = \frac{F (\frac{l}{2})}{AY} + \frac{2 F (\frac{l}{2})}{AY} = \frac{3 Fl}{2 AY}$

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