Thermal Properties of Matter - Result Question 2
2. Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $\ell_1$ and $\ell_2$ respectively. If $(\ell_2-\ell_1)$ is maintained same at all temperatures, which one of the following relations holds good?
[2016, 1999, 1995]
(a) $\alpha_1 \ell _{2_2}=\alpha_2 \ell _{1_2}$
(b) $\alpha_1 \ell_2=\alpha_2 \ell_1$
(c) $\alpha_1 \ell_2=\alpha_2 \ell_1$
(d) $\alpha_1 \ell_1=\alpha_2 \ell_2$
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Answer:
Correct Answer: 2. (d)
Solution:
- (d) From question, $(\ell_2-\ell_1)$ is maintained same at all temperatures hence change in length for both rods should be same
i.e., $\Delta \ell_1=\Delta \ell_2$
As we know, coefficient of linear expansion,
$\alpha=\frac{\Delta \ell}{\ell_0 \Delta T}$
$\ell_1 \alpha_1 \Delta T=\ell_2 \alpha_2 \Delta T$
$\ell_1 \alpha_1=\ell_2 \alpha_2$
