Question

Young's moduli of two wires $A$ and $B$ are in the ratio $7:4$. Wire $A$ is $2\text{m}$ long and has radius $R$. Wire $B$ is $1.5\text{m}$ long and has radius $2\text{mm}$. If the two wires stretch by the same length for a given load, then the value of $R$ is close to,

• A. $1.7\text{mm}$
• B. $1.3\text{mm}$
• C. $1.9\text{mm}$
• D. $1.5\text{mm}$

Answer 1

The correct option is A $1.7\text{mm}$

For an elastic wire, $F=\left(\frac{YA}{l}\right)\Delta l$

$\Rightarrow \Delta l=\frac{Fl}{YA}$

As, $\Delta l_1=\Delta l_2$

$\Rightarrow \frac{F{l}_1}{\pi r_1^2{Y}_1}=\frac{F{l}_2}{\pi r_2^2{Y}_2}$

$\frac{2}{R^2\times 7}=\frac{1.5}{2^2\times 4}$

$\therefore R=1.75\text{mm}$

Hence, $\left(C\right)$ is the correct answer.