Solveeit Logo
Login

Question

Question: Two wires of equal length and cross-section are suspended as shown. Their Young’s modulii are Y<sub>...

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+Y22\frac{Y_{1} + Y_{2}}{2}

C

Y1Y2Y1+Y2\frac{Y_{1}Y_{2}}{Y_{1} + Y_{2}}

D

Y1Y2\sqrt{Y_{1}Y_{2}}

Answer

Y1+Y22\frac{Y_{1} + Y_{2}}{2}

Explanation

Solution

Equivalent spring constant of a wire is given by

K = YAl\frac{YA}{l}

Keq = K1 + K2

or Y(2A)l\frac{Y(2A)}{l} = Y1Al\frac{Y_{1}A}{l} + Y2Al\frac{Y_{2}A}{l}

or Y = Y1+Y22\frac{Y_{1} + Y_{2}}{2}