A metal rod of length L, cross-sectional area A, Young's modulus Y and coefficient of linear expansion is heated to t^ C. The work that can be performed by the rod when heated is

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Correct answer: B. (b): Work done by the rod on heating = Energy stored in the rod W= 12k ( L )^2 Here, length of rod =L, Young's modulus =Y coefficient of linear expansion = , temperature increased t=t ^ C Increase in length of rod, L= Lαt Also, Y= F/A L/L= F L L A F L= YL A ⇒F= ( YAL ) L ∴ k= YAL [ ∵F=k L ]So from eqn. (i), W= 12 ( YAL ) ( Lαt )^2= YA ^2Lt^22

$A metal rod of length L, cross-sectional area A, Young's modulus Y and coefficient of linear expansion α is heated to t^{\circ} C . The work that can be performed by the rod when heated is$

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