Consider the barometer shown in figure (13-Q1). If a small hole is made at a point P in the barometer tube, will the mercury come out from this hole?

The pressure at point P (given by ρgh where h is the height of point P) is less than the atmospheric pressure (given by ρ₀gH where H is the height of the mercury column). The outside pressure is atmospheric pressure. As the pressure at point P is less than atmospheric pressure, the liquid will not flow out.