Properties of Matter 1 Question 14

14. Two rods of different materials having coefficients of thermal expansion α1,α2 and Young’s moduli Y1,Y2 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 α1:α2=2:3, the thermal stresses developed in the two rods are equal provided Y1:Y2 is equal to

(1989, 2M)

(a) 2:3

(b) 1:1

(c) 3:2

(d) 4:9

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Answer:

Correct Answer: 14. (c)

Solution:

  1. Thermal stress σ=YαΔθ

Given, σ1=σ2

Y1α1Δθ=Y2α2Δθ or Y1Y2=α2α1=32



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