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)

$\frac{Y_{1} + Y_{2}}{2}$

Answer 2

Let the equivalent young's modulus of given combination is Y and the area of cross section is 2A.

For parallel combination $k_{1} + k_{2} = k_{eq.}$

$\frac{Y_{1}A}{L} + \frac{Y_{2}A}{L} = \frac{Y2A}{L}$

$Y_{1} + Y_{2} = 2Y$,$\therefore Y = \frac{Y_{1} + Y_{2}}{2}$