In a manometer, the heights of the mercury surfaces in its two arms are 2 cm and 8 cm . The arm exposed to the atmosphere contains the 8 cm surface. The atmospheric pressure is 1.01 10^5 N m ⁻² . Determine the pressure of the mercury at the bottom of the U tube.

Step-by-step solution

Given: Atmospheric pressure, P₀ = 1.01 10^5 N m ⁻² Height of mercury in the open arm from the bottom, h = 8 cm = 0.08 m Density of mercury, = 13.6 10^3 kg m ⁻³ Acceleration due to gravity, g = 9.8 m s ⁻² The pressure at the bottom of the U-tube can be calculated by considering the open arm, which is exposed to the atmosphere. The pressure at the bottom is the sum of the atmospheric pressure and the pressure exerted by the mercury column in the open arm. P_ bottom = P₀ + g h Substituting the given values: P_ bottom