WAEC Physics 2018 Paper

Concept:A liquid barometer works by balancing the pressure of the atmosphere against the hydrostatic pressure of the liquid column.Explanation:For $1.5$ atm, the equivalent mercury height is:$h_{\mathrm{Hg}} = 1.5 \times 76\ \mathrm{cm} = 114\ \mathrm{cm}$Let $h_Q$ be the required height of liquid $Q_1$.Since both columns exert the same pressure:$h_Q \cdot \rho_Q \cdot g = h_{\mathrm{Hg}} \cdot \rho_{\mathrm{Hg}} \cdot g$The $g$ cancels out, giving:$h_Q = \frac{h_{\mathrm{Hg}} \cdot \rho_{\mathrm{Hg}}}{\rho_Q}$$h_Q = \frac{114 \times 13.6}{16.2} = \frac{1550.4}{16.2} \approx 95.7\ \mathrm{cm}$Convert to millimetres:$95.7\ \mathrm{cm} = 957\ \mathrm{mm}$Answer:The least length of the tube is $957\ \mathrm{mm}$.Therefore, the correct option is B. 957mm.