JAMB Physics 2024 Paper

Concept:For two liquids in connected columns, pressure at the same level is equal, so the density of liquid X can be found from the heights and the known density of methanol.Explanation:Density of methanol = $800\,\mathrm{kg\,m^{-3}} = 0.8\,\mathrm{g\,cm^{-3}}$.From the diagram, height of methanol column = $7.1$ and height of liquid X column = $14.2$.Using pressure balance:$$\rho_{\text{methanol}} \times h_{\text{methanol}} \times g = \rho_x \times h_x \times g$$$$0.8 \times 7.1 = \rho_x \times 14.2$$$$\rho_x = \frac{0.8 \times 7.1}{14.2} = 0.4\,\mathrm{g\,cm^{-3}}$$Since relative density here is compared with methanol:$$\text{Relative density of X} = \frac{\rho_x}{\rho_{\text{methanol}}} = \frac{0.4}{0.8} = 0.5$$Answer:B. 0.5