Question

Three bars having lengths l, 2l and 3l and area of cross-section A, 2A and 3A are joined rigidly end to end. Compound rod is subjected to a stretching force F. The increase in length of rod is (Young's modulus of material is Y and bars are massless)

• A. $\frac{13Fl}{2AY}$
• B. $\frac{Fl}{AY}$
• C. $\frac{9Fl}{AY}$
• D. $\frac{3Fl}{AY}$

Answer 1

The correct option is D $\frac{3Fl}{AY}$

Let $x_1,x_2,x_3$ be the individual extensions in rods 1, 2, 3 on application of force 'from' the combination of rods.


Distribution of stretching force and area

$\Rightarrow F_1=F,F_2=F,F_3=F$

$or,x_1=\frac{F_{1}L}{AY}=\frac{FL}{AY}$

$x_2=\frac{2FL}{2AY}$

$x_3=\frac{3FL}{3AY}$

$\Rightarrow x_{net}=x_1+x_2+x_3$

$\therefore x_{net}=\frac{3FL}{AY}$

Tip: For combination of rod joined end to end, the stretching force for each rod will be same.