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Standard XII

Physics

Young's Modulus of Elasticity

Two wires of ...

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

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Solution

The correct option is B
Let the equivalent young's modulus of given combination is Y and the area of cross section is 2A.
For parallel combination $k_{1} + k_{2} = k_{e q}$ .
$\frac{Y_{1} A}{L} + \frac{Y_{2} A}{L} = \frac{Y 2 A}{L}$
$Y_{1} + Y_{2} = 2 Y, ∴ Y = \frac{Y_{1} + Y_{2}}{2}$

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The correct option is B
Let the equivalent young's modulus of given combination is Y and the area of cross section is 2A.
For parallel combination $k_{1} + k_{2} = k_{e q}$ .
$\frac{Y_{1} A}{L} + \frac{Y_{2} A}{L} = \frac{Y 2 A}{L}$
$Y_{1} + Y_{2} = 2 Y, ∴ Y = \frac{Y_{1} + Y_{2}}{2}$