Question

7.
Two rods of different materials having Young's
modulus Y1 and Y2and coefficient of thermal
expansion alpha1 and alpha2 are fixed between two rigid
supports. The rods are heated to the same
temperature if there is no bending of the rods, the
thermal stress developed in these rods are equal
provided

1) Y1/Y2 = √alpha2/alpha1
2) Y1/Y2 = alpha1/alpha2
3) Y1/Y2 = √alpha1/alpha2
4) Y1/Y2 = alpha2/alpha1
​

Answer 1

Y=FL/A∆L

∆L = L(alpha)∆T

thus,

Y1/Y2 = alpha2/alpha1