JAMB Physics 2019 Paper

Concept:In Hare's apparatus, the pressure exerted by each liquid column must be equal for the system to be in equilibrium.Explanation:The pressure due to a liquid column is given by $P = \rho g h$.For the two limbs, equate the pressures:$\rho_{\text{water}} g h_{\text{water}} = \rho_{\text{kerosine}} g h_{\text{kerosine}}$Since $g$ is the same on both sides, it cancels out:$\rho_{\text{water}} h_{\text{water}} = \rho_{\text{kerosine}} h_{\text{kerosine}}$Substitute the given values:$1.0 \times 20.0 = 0.80 \times h_{\text{kerosine}}$$20.0 = 0.80\,h_{\text{kerosine}}$$h_{\text{kerosine}} = \dfrac{20.0}{0.80} = 25.0$ cmThe kerosine column is taller than the water column because kerosine has a lower density.Answer:The height of the kerosine column is $25.0$ cm.