Question

Two wires A and B have young's modulii in the ratio $1:2$ and ratio of the lengths is $1:1$. under the application of same stress the ratio of elongation is

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

Answer 1

Answer: (C)

$2:1$

Given,

$Y_A:Y_B=1:2$

$l_A:l_B=1:1$

Stress, $s=\frac{F}{A}$

Young's modulus,

$Y=\frac{F/A}{\Delta l/l}$

$Y\propto \frac{l}{\Delta l}$

$\Delta l\propto \frac{l}{Y}$

$\frac{\Delta l_A}{\Delta l_B}=\frac{l_A}{l_B}.\frac{Y_B}{Y_A}$

$\frac{\Delta l_A}{{\Delta }_B}=\frac{1}{1}.\frac{2}{1}=\frac{2}{1}$

$\Delta l_A:\Delta l_B=2:1$

The correct option is B.