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

Answer: (B)

Spring constant of a wire is given by
$k=\frac{YA}{l}$
Refer figure. The equivalent spring constant of wire is
$k_{eq}=k_{1}+k_{2}$
or $\frac{Y\left(2A\right)}{l}=\frac{Y_{1}A}{l}+\frac{Y_{2}A}{l}$ or $Y=\frac{Y_{1}+Y_{2}}{2}$