Two rods of different materials having co- efficient of linear expansion $α_{1}, α_{2}$ 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 $α_{1} : α_{2} = 2 : 3$ , The thermal stress developed in the two rods are equally provided y₁ / y₂ is equal to.

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3:2

4:9

1:1

2:3

answer is C.

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Detailed Solution

We know that,

$Δ l = l α Δ T i e, \frac{Δ l}{l} = α Δ T S t r e s s = Y x s t a i n s t r e s s = Y α Δ T$

In case of the first rod,

$Y_{1} α_{1} ∆ T$

similarly in the case of the second rod,

$Y_{2} α_{2} ∆ T$

Since stresses are equal,

$Y_{1} α_{1} ∆ T$ = $Y_{2} α_{2} ∆ T$

$\frac{Y_{1}}{Y_{2}} = \frac{α_{2}}{α_{1}} = \frac{3}{2}$

Hence the correct answer is 3:2.

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