A vertical U-tube of uniform cross-section contains mercury (relative density 13.6). A column of water 35.2 cm long is poured into the left arm and a…

The heavier column (water, $35.2\ \mathrm{cm}$, pressure head $35.2$ in water-cm) pushes the left mercury surface down. Take the level of the lower mercury surface (left arm) as reference. The pressure there from the left is $35.2\times1$ in water-cm. On the right, the same horizontal level lies a distance $h$ below the upper mercury surface, so the pressure is $10.0\times0.8 + 13.6\,h$. Equating: $35.2 = 8 + 13.6h$, giving $h = 27.2/13.6 = 2.0\ \mathrm{cm}$. Neglecting the oil gives $2.6\ \mathrm{cm}$, and adding the oil head instead of subtracting it gives $3.2\ \mathrm{cm}$.