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 α. The bar is heated so that its temperature increases by θ°C. Then the force exerted at the ends of the bar is given by

Question

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 α. The bar is heated so that its temperature increases by θ°C. Then the force exerted at the ends of the bar is given by

Infinity Learn · Accepted Answer

The coefficient of linear expansion is defined asα$$=$$ increase in length  original length × temp.rise $$=lL$$θ∴ Increase in length $$l=$$αLθ. $$NowY=FLAlF=YAlL=YA$$αLθ$$L=YA$$αθHence the correct choice is (3).

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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 α. The bar is heated so that its temperature increases by θ°C. Then the force exerted at the ends of the bar is given by

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