JAMB Physics 2010 Paper

Concept:Linear expansion is directly proportional to the original length and the linear expansivity when the temperature change is the same.Explanation:Let $\alpha_P$ and $\alpha_Q$ be the linear expansivities of P and Q.Given: $\frac{\alpha_P}{\alpha_Q} = \frac{2}{3}$ and $\frac{l_P}{l_Q} = \frac{3}{4}$.The increase in length of each metal is $\Delta l = \alpha l \Delta \theta$.Since both metals are heated through the same temperature difference, $\Delta \theta$ is constant and cancels out.Thus, the ratio of their increases in length is:$$\frac{\Delta l_P}{\Delta l_Q} = \frac{\alpha_P l_P}{\alpha_Q l_Q} = \frac{2}{3} \times \frac{3}{4} = \frac{1}{2}.$$Therefore, the ratio of the increase in length of P to Q is $1:2$.Answer:$1:2$