Question

Two wires of equal length and cross-section are suspended as shown. Their Young’s modulii 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 $\frac{Y_1+Y_2}{2}$

Let the equivalent young's modulus of given combination is Y and the area of cross section is 2A.
For parallel combination $k_1+k_2=k_{eq}$.
$\frac{Y_{1}A}{L}+\frac{Y_{2}A}{L}=\frac{Y2A}{L}$
$Y_1+Y_2=2Y,\therefore Y=\frac{Y_1+Y_2}{2}$