A metal beam having coefficient of linear expansion $ \alpha $ Youngs modulus $ Y $ , area of across section a and length L, is clamped at both ends. After cooling by $ t{}^\circ C, $ the force exerted in the clamp is

Updated On: Jun 14, 2022

$ YL\alpha t $
$ Y\alpha a $
$ YaL\alpha t $
$ Ya\alpha t $

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The Correct Option is D

Solution and Explanation

: $ Y=\frac{F}{a}\times \frac{L}{l} $ where a = area or $ F=Yal/L $ ................ (i) $ \alpha =\frac{Change\text{ }in\text{ }length\,(l)}{original\text{ }length(L)\times temperature\text{ }change(l)} $ or $ \alpha =\frac{l}{Lt} $ .................. (ii) $ \therefore $ $ F=Ya\alpha t. $

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