Two rods of different materials having coefficients of thermal expansions Î±1 and Î±2 and Youngâs moduli Y1 and Y2 respectively are fixed between two rigid walls. The rods are heated, such that they undergo the same increase in temperature. There is no bending of rods. If Î±1/Î±2 = 2/3 and stresses developed in the two rods are equal, then (Y1/Y2) is :

Question

Two rods of different materials having coefficients of thermal expansions Î±1 and Î±2 and Youngâs moduli Y1 and Y2 respectively are fixed between two rigid walls. The rods are heated, such that they undergo the same increase in temperature. There is no bending of rods. If Î±1/Î±2 = 2/3 and stresses developed in the two rods are equal, then (Y1/Y2) is : (A)  3/2  (B)  1  (C)  2/3  (D)  1/2

Tardigrade Admin · Accepted Answer

Thermal stress is a measure of the internal distribution of force per unit area within a body that is applied to the body, in the form of heat.
Thermal stress

= Y α Δ T

where

Y

is Young's modulus,

α

the coefficient of linear expansion and

Δ T

the change in temperature.
Both the rods are heated,

∴ Y_{1} α_{1} Δ T_{1} = Y_{2} α_{2} Δ T_{2}

Since,

Δ T_{1} = Δ T_{2}

\Rightarrow \frac{Y _{1}}{Y _{2}} = \frac{α _{2}}{α _{1}} = \frac{3}{2}

$3/2$

$1$

$2/3$

$1/2$