Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

The coefficients of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$ , 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?

$\alpha_1 l_2^2 = \alpha_2 l_1^2$

$\alpha_1^2 l_2 = \alpha_2^2 l_1$

$\alpha_1 l_1 = \alpha_2 l_2$

$\alpha_1 l_2 = \alpha_2 l_1$

Step-by-Step Solution

For the difference in lengths $(l_2 - l_1)$ to remain constant at all temperatures, the change in length of both rods must be equal for any given change in temperature $\Delta T$ . Let the change in length of the brass rod be $\Delta l_1$ and that of the steel rod be $\Delta l_2$ . We know that $\Delta l = l \alpha \Delta T$ . So, $\Delta l_1 = l_1 \alpha_1 \Delta T$ and $\Delta l_2 = l_2 \alpha_2 \Delta T$ . Since $\Delta l_1 = \Delta l_2$ , we have: $l_1 \alpha_1 \Delta T = l_2 \alpha_2 \Delta T$ $\alpha_1 l_1 = \alpha_2 l_2$

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