The bar shown in the figure is made of a single piece of material. It is fixed at one end. It consists of two segments of equal length \frac{L_{0}}{2} but different cross-sectional area A and 2A. What is the change in length of the entire system under the action of an axial force F. Consider the shape of joint to remain circular. (Given : y is young's modulus).

Engineering

Physics

Newtons Second Law of Motion

Free Body Diagram

Stress Strain and Hookes Law New

Question

The bar shown in the figure is made of a single piece of material. It is fixed at one end. It consists of two segments of equal length $\frac{L_{0}}{2}$ but different cross-sectional area A and 2A. What is the change in length of the entire system under the action of an axial force F. Consider the shape of joint to remain circular. (Given : y is young's modulus).

$\frac{3 FL}{8 Ay}$

$\frac{3 FL}{2 Ay}$

None of these

$\frac{3 FL}{4 Ay}$

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F = $\frac{YA}{L / 2} \cdot {ΔL}_{1}$ ∴ ΔL₁+ ΔL₁ = $\frac{3 FL}{4 YL}$
F = $\frac{Y \cdot 2 A}{L / 2} \cdot {ΔL}_{2}$