Question

two wires of equal length and cross sectional area are suspended vertically. Their young modulii are Y1 and Y2 respectively. The equivalent young's modulii will be

Answer 1

The equivalent young's moduli will be $\mathrm{Y}_{\mathrm{eq}}=\frac{\mathrm{Y}_{1}+\mathrm{Y}_{2}}{2}$

Explanation:

To get the answer, lets see the formula for young modulus e.g.

$\mathrm{k}=\frac{\mathrm{YA}}{\mathrm{L}}$

For string one

$k_{1}=\frac{Y_{1} A}{L}$

For string two

$\mathrm{k}_{2}=\frac{\mathrm{Y}_{2} \mathrm{~A}}{\mathrm{~L}}$

Since, $k_{1}$ and $k_{2}$ are parallel, then

$\mathrm{k}_{\mathrm{eq}}=\mathrm{k}_{1}+\mathrm{k}_{2}$

$\frac{Y_{e q}(2 A)}{L}=\left(Y_{1}+Y_{2}\right) \frac{A}{L}$

Thus, the equivalent young's modulii will be

$\mathrm{Y}_{\mathrm{eq}}=\frac{\mathrm{Y}_{1}+\mathrm{Y}_{2}}{2}$