Two rods of different materials having coefficient of linear expa… - Vidyadip

MCQ

Two rods of different materials having coefficient of linear expansion $\alpha_1$and $\alpha_2$ and Young's modulii $Y_1$ and $Y_2$ 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 rods. If $\alpha_1:\alpha_2= 2 : 3$, the thermal stress developed in two rods are equal provided $Y_1 : Y_2$ is equal to

A
$2:3$
B
$4:9$
C
$1:1$
✓
$3:2$

✓

Answer

Correct option: D.

$3:2$

d
$F=y A \propto(\Delta t)=\left(\frac{F}{A}\right)=y \propto \Delta t$

$y \propto=$ const $\Rightarrow y \propto \frac{1}{\alpha}$

$\frac{y_{1}}{y_{2}}=\frac{\alpha_{2}}{\alpha_{1}}$

$\frac{y_{1}}{y_{2}}=\frac{3}{2}$

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