A simple U tube contains mercury to the same level in both of its arms. If water is poured to a height of 13.6 cm in one arm, how much will be the rise in mercury level in other arm? Density of mercury $13.6\times {10}^{3}kg/m^3$ and density of water = $1000kg/m^3$.

Initially, the length of mercury columns in two arms is equal. Height to which water is poured in one arm, h = 13.6 cm Density of mercury = 13.6 × 103 kg m-3 Density of water = 103 kg m-3 Pouring 13.6 cm water, the mercury level goes down to A, by x cm in the left arm and rises to C, by x cm in the right arm. So, BC=2x cm Pressure at level A = Pressure at level B or 13.6 × 103 × g = 2x × 13.6 × 103 × g 2x = 1 cm The rise in mercury level in the other arm will be x= 0.5 cm.