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  • A metal bar of length L and area of cross-section A is rigidly clamped between two walls. The Young's modulus of its material is Y and the coefficient of linear expansion is <img

A metal bar of length L and area of cross-section A is rigidly clamped between two walls. The Young's modulus of its material is Y and the coefficient of linear expansion is \mathrm{\alpha.} The bar is heated so that its temperature increases by \mathrm{\theta^{\circ} \mathrm{C}}. Then the force exerted at the ends of the bar is given by

Option: 1

\mathrm{Y L \, \, \alpha\, \, \theta}


Option: 2

\mathrm{Y L \, \, \alpha\, \, \theta/A}


Option: 3

\mathrm{Y A \, \, \alpha\, \, \theta}


Option: 4

\mathrm{Y \theta \, \, \alpha/ LA}


Answers (1)

best_answer

The coefficient of linear expansion is defined as

\mathrm{ \alpha=\frac{\text { increase in length }}{\text { original length } \times \text { temp.rise }}=\frac{l}{L \theta} }

\mathrm{\therefore \quad Increase in length\, \, l=\alpha \, \, L \, \, \theta}. Now

        Or                      \mathrm{ \begin{aligned} & Y=\frac{F L}{A l} \\\\ & F=\frac{Y A l}{L}=\frac{Y A \alpha L \theta}{L}=Y A \alpha \theta \end{aligned} }

Posted by

vishal kumar

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