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Two rods of different materials having c...

Two rods of different materials having coefficients of thermal expansion `alpha_1`, `alpha_2` and Young's modulii `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

A

`2:3`

B

`1:1`

C

`3:2`

D

`4:9`

Text Solution

Verified by Experts

The correct Answer is:
C
`"Stress"/"Strain"` and `/_\lpropl//A`
`:.` Strain `(/_\l)/lalpha/_\Timplies` Stress `=Yalpha/_\T`
For first rod, stress `=gamma_(1)alpha_(1)/_\T`. For the second rod, stress
`=gamma_(2)alpha_(2)/_\T`. Since stresses are equal. Therefore,
`gamma_(1)alpha_(1)/_\T`
`implies(Y_(1))/(Y_(2))=(alpha_(2))/(alpha_(1))=3/2`
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