A metal rod of Young's modulus 'Y' and coefficient of linear expansion ' $\propto^{\prime}$ has its…

A metal rod of Young's modulus 'Y' and coefficient of linear expansion ' $\propto^{\prime}$ has its temperature raised by ' $\Delta \theta^{\prime} .$ The linear stress to prevent the expansion of rod is (L and $\ell$ is original length of rod and expansion respectively)
  1. $\mathrm{Y} \frac{\mathrm{L}}{\ell}$
  2. $\frac{Y \propto}{\Delta \theta}$
  3. $\mathrm{Y} \propto \Delta \theta$
  4. $\mathrm{Y}\left(\frac{\ell}{\mathrm{L}}\right)^{2}$

Solution

For thermal expansion $\Delta \mathrm{L}=\mathrm{L} \Delta \theta$ If rod is compress by $\Delta \mathrm{L}$ then $\begin{aligned} \Delta \mathrm{L}=& \frac{\mathrm{FL}}{\mathrm{AY}} \\ \therefore \frac{\mathrm{FL}}{\mathrm{AY}} &=\mathrm{L} \propto \Delta \theta \quad \therefore \frac{\mathrm{F}}{\mathrm{A}}=\mathrm{Y} \propto \Delta \theta \end{aligned}$

Asked in: MHT CET 2020 (13 Oct Shift 2)

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