Three identical vessels A, b and C are filled with water, mercury and kerosene respectively up to an equal height bottom of the vessels are provided with identical taps at the bottom of the vessels. If the three taps are opened simultaneously then which vessel is emptied first?

1. The rate at which a liquid flows out of a tap at the bottom of a vessel depends on the pressure at the bottom and the properties of the liquid (density and viscosity), according to Torricelli's law and Poiseuille's law. 2. Assuming the taps are identical and the height is the same, the pressure exerted by the liquid column (hydrostatic pressure) is proportional to the density of the liquid ($P = h \rho g$). Mercury has the highest density, followed by water, and then kerosene. 3. However, the outflow rate (efflux velocity) according to Torricelli's law ($v = \sqrt{2gh}$) depends only on height (h) and gravity (g), suggesting they should empty at the same rate if viscosity is ignored. 4. Considering viscosity and density's effect on flow rate through an orifice (tap), liquids with lower density and lower viscosity tend to flow out faster. Kerosene has a significantly lower density and lower viscosity compared to water and mercury. Therefore, Vessel C (containing kerosene) will be emptied first.