Two rods of different materials with coefficients linear thermal expansion `alpha_(1), alpha_(2)`, and Young's moduli `Y_(1)` and `Y_(2)`, respectively are fixed between two rigid walls. They are heated to have the same increase in temperature . If the rods do not bend and if `alpha_(1) : alpha_(2) = 2 : 3`, then thermal stresses developed in the two rods will be equal when `Y_(1) : Y_(2)` ie equal to

Options

A. `2 : 3`
B. `2 : 5`
C. `3 : 2`
D. `5 : 2`

Answer

c

Explanation

Thermal stress = Y `xx` strain
or `S = Y epsilon` or `S = Y alpha t`
Where `alpha` = linear thermal expansion, Y = Young's modulus Here, `S_(1) = S_(2) implies Y_(1) alpha_(1) t = y_(2) alpha_(2) t`
or `(y_(1))/(y_(2)) = (alpha_(2))/(alpha_(1)) = (3)/(2)`
Thus, `y_(1),y_(2) = 3 : 2`