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» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>:3`<br/>`1:1`<br/>`3:2`<br/>`4:9`<br/></p>Solution :Expansion in the rod due to <a href="https://interviewquestions.tuteehub.com/tag/rise-1189674" style="font-weight:bold;" target="_blank" title="Click to know more about RISE">RISE</a> in temp Compression in rod. For the first rod`Deltal_(1)=alpha_(1)l_(1)Deltatheta` <br/> Compression in the rod `Deltal_(1)= (-F)/(A) (l_(1))/(Y_(1))` <br/> or the length of the rod remains unchanged <br/> `alpha_(1)l_(1)<a href="https://interviewquestions.tuteehub.com/tag/delta-947703" style="font-weight:bold;" target="_blank" title="Click to know more about DELTA">DELTA</a> theta= (-Fl_(1))/(AY_(1))` <br/> or <br/> `alpha_(1) Delta theta = (-F)/(AY_(1))--- (i)` <br/> Similarly for second rod <br/> `alpha_(2) Delta theta = (-F)/(AY_(2))--- (ii)` <br/>`(alpha_(1))/(alpha_(2))=(Y_(2))/(Y_(1))or(Y_(1))/(Y_(2))=(alpha_(2))/(alpha_(1))=(3)/(2)`</body></html>