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» `(alpha t )/(F)` `(Y)/(alpha t)` `Y prop t ` `(1)/(Y prop t)` Solution :`DELTA l = alpha l Delta T` `therefore (Delta l )/(l) = alpha Delta T ""...(1)` YOUNG modulus `Y = ("stress" SIGMA _(l))/("STRAIN" G_(l))` `therefore epsi _(l ) = (sigma _(l))/(Y)` `therefore (Delta l )/(l) = (sigma _(l))/( Y) ""...(2)` From equation (1) and (2) `(sigma _(1))/(Y) = alpha Delta T` `therefore sigma _(l) = Y prop Delta T` `therefore sigma _(l) = Y prop T` (where `Delta T =l ^(@)C)`