Question

Two wires of equal length and cross-section area suspended as shown in figure. Their Young's modulus are$Y_1$ and $Y_2$ respectively. The equivalent Young's modulus will be

• A. $Y_1+Y_2$
• B. $\frac{Y_1+Y_2}{2}$
• C. $\frac{Y_1{Y}_2}{Y_1+Y_2}$
• D. $\sqrt{Y_1{Y}_2}$

Answer 1

The correct option is B $\frac{Y_1+Y_2}{2}$

We know that

$K=\frac{F}{△l}$ = $\frac{YA}{l}$

and, $K_{eq}=k_1+k_2$

$\Rightarrow$ $\frac{Y_{eq}2A}{l}$ =$\frac{Y_{1}A}{l}$ + $\frac{Y_{2}A}{l}$

$\Rightarrow$ $Y_{eq}=\frac{Y_1+Y_2}{2}$