JAMB Physics 2019 Paper

Concept:Linear expansivity measures how much a material's length changes when its temperature changes by one degree.Explanation:Given: initial length $L_1 = 100\,\text{cm}$, initial temperature $T_1 = 200^{\circ}\mathrm{C}$.Final length $L_2 = 99.4\,\text{cm}$, final temperature $T_2$ is unknown.Linear expansivity $\alpha = 2 \times 10^{-5} \, {}^\circ\mathrm{C}^{-1}$.Use the formula: $\alpha = \frac{L_2 - L_1}{L_1(T_2 - T_1)}$.Substitute the known values: $2 \times 10^{-5} = \frac{99.4 - 100}{100(T_2 - 200)}$.Compute the change in length: $99.4 - 100 = -0.6$.So $2 \times 10^{-5} = \frac{-0.6}{100(T_2 - 200)}$.Rearrange: $100(T_2 - 200)(2 \times 10^{-5}) = -0.6$.Simplify: $0.002(T_2 - 200) = -0.6$Therefore $T_2 - 200 = \frac{-0.6}{0.002} = -300^{\circ}\mathrm{C}$.Finally, $T_2 = 200 - 300 = -100^{\circ}\mathrm{C}$.Answer:The required temperature is $-100^{\circ}\mathrm{C}$.So the correct option is $D$.