Question:medium

The Young's modulus and Poisson's ratio of a material are respectively Y and $\sigma$. The force required to decrease the area of cross-section of a wire made of this material by $\Delta A$ is

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Remember the definitions of the elastic moduli. Young's Modulus ($Y$) relates tensile stress and strain. Poisson's Ratio ($\sigma$) relates the lateral (sideways) strain to the longitudinal (lengthwise) strain. For small changes, the fractional change in area is twice the fractional change in radius: $\frac{\Delta A}{A} = 2\frac{\Delta r}{r}$.

Updated On: Mar 30, 2026

$\frac{Y\Delta A}{4\sigma}$
$\frac{2Y\Delta A}{\sigma}$
$\frac{Y\Delta A}{2\sigma}$
$\frac{Y\Delta A}{\sigma}$

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The Correct Option is C

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