Question

A uniform rod made of material of Young’s modulus of elasticity $Y$ is subjected to forces shown in the diagram. If $A$ is the area of cross section of the rod, then find its extension

• A. $\frac{3Fl}{AY}$
• B. $\frac{Fl}{AY}$
• C. $\frac{2Fl}{AY}$
• D. $\frac{Fl}{3AY}$

Answer 1

The correct option is C $\frac{2Fl}{AY}$

To approach this type of question,consider the rod into two equal parts.
So elongation due force on left part, $\Delta x_1=\frac{FAl}{2Y}$

Similarly, elongation due to force on right part , $\Delta x_2=\frac{3FAl}{2Y}$
Total elongation of the rod,
$\Delta x=\Delta x_1+\Delta x_2=\left(\frac{F+3F}{2AY}\right)l=\frac{2Fl}{AY}$

Hence, option $\left(c\right)$ is correct.