A U-tube of uniform cross-section stands vertically and contains some mercury, of relative density $13.6$. Water is poured slowly into the left arm until the column of water above the mercury in that arm is $27.2\ \text{cm}$ tall, as shown in the figure. The water and mercury do not mix. How far above the mercury surface in the right arm is the top of the water in the left arm?

Fig. 1: A U-tube with mercury at the bottom. The left arm holds a 27.2 cm column of water above the mercury, and the mercury in the right arm stands higher than the boundary between water and mercury.