Q107 / 180 · NEET 2016 (Phase 1) · Physics

Coefficient of linear expansion of brass and steel rods are $α_{1}$ and $α_{2}$ . Lengths of brass and steel rods are $l_{1}$ and $l_{2}$ , respectively. If $(l_{2} - l_{1})$ is maintained the same at all temperatures, which one of the following relations holds good?

Solution

The difference in length is the same, so the increase in length is equal,

$∆ l_{1} = ∆ l_{2}$

$l_{1} α_{1} ∆ T = l_{2} α_{2} ∆ T$

$\Rightarrow l_{1} α_{1} = l_{2} α_{2}$ .

Hence, the correct answer is option: 'D'.