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Q.

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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a

YLαθ

b

YLαθ/A

c

YAαθ

d

Yθα/LA

answer is C.

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Detailed Solution

The coefficient of linear expansion is defined asα= increase in length  original length × temp.rise =lLθ∴ Increase in length l=αLθ. NowY=FLAlF=YAlL=YAαLθL=YAαθHence 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