Question

A mild steel bar is in two parts having equal lengths. The area of cross-section of Part-1 is double that of Part-2. If the bar carries an axial load P, then the ratio of elongation in Part-1 to that in Part-2 will be

• A. $2$
• B. $4$
• C. $1/2$
• D. $1/4$

Answer 1

The correct option is C $1/2$

$\frac{{\Delta }_1}{{\Delta }_2}=\frac{L_1}{L_2}\times \frac{A_2}{A_1}$
Since, $L_1=L_2$ and $A_1=2A_2$
$\therefore \frac{{\Delta }_1}{{\Delta }_2}=1\times \frac{1}{2}=\frac{1}{2}$