Question

Two wires A and B of the same dimensions are under loads of $4$ and $5.5kg$ respectively. The ratio of Young's modulii of the materials of the wires for the same elongation is:

• A. $64:121$
• B. $\sqrt{11}:\sqrt{8}$
• C. $11:8$
• D. $8:11$

Answer 1

The correct option is D $8:11$

$Y=\frac{F/A}{△l/l}$
$Y_A=\frac{F_A/A}{△l/l}...........................1$
$Y_B=\frac{F_B/A}{△l/l}...........................2$
Dividing 1 and 2
$\frac{Y_A}{Y_B}=\frac{F_A}{F_B}=\frac{4}{5.5}=\frac{8}{11}$