Question

Three bars having length $l, 2 l$ and $3 l$ and area of cross-section $A, 2 A$ and $3 A$ 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. $\frac{13 F I}{2 A Y}$
• B. $\frac{F I}{A Y}$
• C. $\frac{9 F l}{A Y}$
• D. $\frac{3 F l}{A Y}$

Answer 1

Answer: (D)

If extension of rod $=x$
$x=x_{1}+x_{2}+x_{3}$
Where $x_1, x_2, x_3$ are individual extensions in rod $1, 2, 3$
$x_{1}=\frac{F l}{A Y}, x_{2}=\frac{2 F l}{2 A Y}, x_{3}=\frac{3 F l}{3 A Y}$
So $x=\frac{3 F l}{A Y}$