Questions

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 $\mathrm{\theta }$°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
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detailed solution

Correct option is C

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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