Question

A-3 Two wire of equal length and cross-sectional area suspended as shown in figure. Their Young's modulus are $Y_{1}and{Y}_2$ respectively. The equivelent 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 $\frac{Y_1+Y_2}{2}$

Consider whole combination a single rod

$\begin{array}{c}Y=\frac{FL}{2A\ell }=\frac{\left(F_1+F_2\right)L}{2A\ell }=\frac{F_{1}L}{1A\ell }\\ =\frac{Y_1}{2}+\frac{Y_2}{2}=\frac{Y_1+Y_2}{2}\end{array}$