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Q.

Two rods of different materials having co- efficient of linear expansion α1,α2 and Young’s modulii  y1 and y2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increases in temperature. There is no bending of rods. If α1:α2=2:3 , The thermal stress developed in the two rods are equally provided y1 / y2 is equal to. 

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a

2:3

b

1:1

c

3:2

d

4:9

answer is C.

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Detailed Solution

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We know that,

Δl=lαΔT  ie,    Δll  =αΔT  Stress =Y x stain  stress=YαΔT

In case of the first rod,

Y1α1T

similarly in the case of the second rod,

Y2α2T

Since stresses are equal,

Y1α1T=Y2α2T

Y1Y2=α2α1=32

Hence the correct answer is 3:2.

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