A metal rod of Young's modulus and coefficient of thermal expansion alpha is held at its two ends such that its length remains invariant. If its temperature is raised by t^(@)C, the linear stress developed it its is .....

A metal rod of Young's modulus and coefficient of thermal expansion al

1.	A metal rod of Young's modulus and coefficient of thermal expansion alpha is held at its two ends such that its length remains invariant. If its temperature is raised by t^(@)C, the linear stress developed it its is .....
Answer» <html><body><p>`(alpha t )/(F)`<br/>`(Y)/(alpha t)`<br/>`Y prop t `<br/>`(1)/(Y prop t)`</p>Solution :`<a href="https://interviewquestions.tuteehub.com/tag/delta-947703" style="font-weight:bold;" target="_blank" title="Click to know more about DELTA">DELTA</a> l = alpha l Delta T` <br/> `therefore (Delta l )/(l) = alpha Delta T ""...(1)` <br/> <a href="https://interviewquestions.tuteehub.com/tag/young-749721" style="font-weight:bold;" target="_blank" title="Click to know more about YOUNG">YOUNG</a> modulus `Y = ("stress" <a href="https://interviewquestions.tuteehub.com/tag/sigma-1207107" style="font-weight:bold;" target="_blank" title="Click to know more about SIGMA">SIGMA</a> _(l))/("<a href="https://interviewquestions.tuteehub.com/tag/strain-17653" style="font-weight:bold;" target="_blank" title="Click to know more about STRAIN">STRAIN</a>" G_(l))` <br/> `therefore epsi _(l ) = (sigma _(l))/(Y)` <br/> `therefore (Delta l )/(l) = (sigma _(l))/( Y) ""...(2)` <br/> From equation (1) and (2) <br/> `(sigma _(1))/(Y) = alpha Delta T` <br/> `therefore sigma _(l) = Y prop Delta T` <br/> `therefore sigma _(l) = Y prop T` (where `Delta T =l ^(@)C)`</body></html>