Two rods of different materials having coefficients of thermal expansion alpha_(1) , alpha_(2) and Young's Moduli Y_(1), Y_(2) respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If alpha_(1) : alpha_(2) = 2 : 3, the thermal stresses developed in the two rods are equal provided Y_(1) : Y_(2) is equal to

Two rods of different materials having coefficients of thermal expansi

1.	Two rods of different materials having coefficients of thermal expansion alpha_(1) , alpha_(2) and Young's Moduli Y_(1), Y_(2) respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If alpha_(1) : alpha_(2) = 2 : 3, the thermal stresses developed in the two rods are equal provided Y_(1) : Y_(2) is equal to
Answer» `2:3` `1:1` `3:2` `4:9` Solution :Expansion in the rod due to RISE in temp Compression in rod. For the first rod`Deltal_(1)=alpha_(1)l_(1)Deltatheta` Compression in the rod `Deltal_(1)= (-F)/(A) (l_(1))/(Y_(1))` or the length of the rod remains unchanged `alpha_(1)l_(1)DELTA theta= (-Fl_(1))/(AY_(1))` or `alpha_(1) Delta theta = (-F)/(AY_(1))--- (i)` Similarly for second rod `alpha_(2) Delta theta = (-F)/(AY_(2))--- (ii)` `(alpha_(1))/(alpha_(2))=(Y_(2))/(Y_(1))or(Y_(1))/(Y_(2))=(alpha_(2))/(alpha_(1))=(3)/(2)`