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Two rods of different materials having coefficients of thermal expansion a 1, a 2 and Young’s modulii Y 1, Y 2 respectively are fixed between two rigid massive walls. The rods are temperature. There is no bending of the rods. If a 1 :a 2= 2:3, the thermal stresses developed in the two rods are equal provided Y 1: Y 2 is equal to (a) 2:3 (b) 1:1 (c) 3:2 (d) 4:9

 Two rods of different materials having coefficients of thermal expansion a1, a2 and Young’s modulii Y1,Y2 respectively are fixed between two rigid massive walls. The rods are temperature. There is no bending of the rods. If a1:a2=2:3, the thermal stresses developed in the two rods are equal provided Y1:Y2 is equal to
(a) 2:3
(b) 1:1
(c) 3:2
(d) 4:9

Grade:12th pass

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago

(c) ?l­ = la?T ? ?l/l = a?T

Stress = Y * strain

? Stress = Ya?T

For first rod stress = Y1a1?T

For first rod stress = Y1a1?T

For second rod stress = Y2a2?T

Since, stress are equal

? Y1a1?T = Y2a2?T

Or, Y1/Y2 = a2/a1 = 3/2

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