Two wires of equal length and cross-section are suspended as shown. Their Young’s modulii are Y1 and Y2 respectively. The equivalent Young’s modulus will be

Question

Two wires of equal length and cross-section are suspended as shown. Their Young’s modulii are Y1 and Y2 respectively. The equivalent Young’s modulus will be (A) Y1+Y2 (B) (Y1+Y2/2) (C) (Y1Y2/Y1+Y2) (D) √Y1Y2

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/c8bbc29a9b1d1533e43bb717868a8266-.png" /> Spring constant of a wire is given by k=(YA/l) Refer figure. The equivalent spring constant of wire is keq=k1+k2 or (Y(2A)/l)=(Y1A/l)+(Y2A/l) or Y=(Y1+Y2/2)

Q. 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

$Y_{1} + Y_{2}$

$\frac{Y _{1} + Y _{2}}{2}$

$\frac{Y _{1} Y _{2}}{Y _{1} + Y _{2}}$

$Y_{1} Y_{2}$

Spring constant of a wire is given by
$k = \frac{Y A}{l}$
Refer figure. The equivalent spring constant of wire is
$k_{e q} = k_{1} + k_{2}$
or $\frac{Y ( 2 A )}{l} = \frac{Y _{1} A}{l} + \frac{Y _{2} A}{l}$ or $Y = \frac{Y _{1} + Y _{2}}{2}$

Q. Two wires of equal length and cross-section are suspended as shown. Their Young’s modulii are Y1​ and Y2​ respectively. The equivalent Young’s modulus will be

Y1​+Y2​

2Y1​+Y2​​

Y1​+Y2​Y1​Y2​​

Y1​Y2​​