WAEC Physics 2016 Paper

Concept:Linear expansion is the increase in length of a solid when its temperature increases.Explanation:Given: initial length $L_1 = 1.8\,\mathrm{m}$, initial temperature $\theta_1 = 10^\circ\mathrm{C}$, change in length $\Delta L = 0.007\,\mathrm{m}$, and linear expansivity $\alpha = 2.3 \times 10^{-5}\,\mathrm{K}^{-1}$.The formula for linear expansion is:$$\Delta L = \alpha L_1 (\theta_2 - \theta_1)$$Substitute the known values:$$0.007 = (2.3 \times 10^{-5})(1.8)(\theta_2 - 10)$$Rearrange to find the temperature rise:$$\theta_2 - 10 = \frac{0.007}{2.3 \times 10^{-5} \times 1.8}$$Calculate the denominator:$$2.3 \times 10^{-5} \times 1.8 = 4.14 \times 10^{-5}$$So:$$\theta_2 - 10 = \frac{0.007}{4.14 \times 10^{-5}} \approx 169.08$$Therefore, final temperature:$$\theta_2 = 169.08 + 10 = 179.08^\circ\mathrm{C}$$Answer:The rod is heated to about $179^\circ\mathrm{C}$.Correct option: D.