Properties of Matter 1 Question 14
14. Two rods of different materials having coefficients of thermal expansion $\alpha _1, \alpha _2$ and Young’s moduli $Y _1, Y _2$ 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
(1989, 2M)
(a) $2: 3$
(b) $1: 1$
(c) $3: 2$
(d) $4: 9$
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Answer:
Correct Answer: 14. (c)
Solution:
- Thermal stress $\sigma=Y \alpha \Delta \theta$
Given, $\quad \sigma _1=\sigma _2$
$\therefore \quad Y _1 \alpha _1 \Delta \theta=Y _2 \alpha _2 \Delta \theta$ or $\frac{Y _1}{Y _2}=\frac{\alpha _2}{\alpha _1}=\frac{3}{2}$
