An air column 10cm in length is trapped into the sea end of a capillary tube by a 15cm column of mercury with the tube held vertically as shown above. On inverting the tube the air column becomes 15cm long. The atmospheric pressure during the experiment is
To determine the atmospheric pressure during the experiment, we can use the concept of balancing pressures.
Initially, when the tube is held vertically as shown, the pressure at the sea end of the capillary tube is atmospheric pressure (P) plus the pressure due to the column of mercury (h.mg), where h is the height of the mercury column and m is the density of mercury.
On inversion, the air column moves to the top of the tube, and now the pressure at the air column end is atmospheric pressure (P) plus the pressure due to the column of mercury at that end (15 cm in this case). The pressure at the sea end is now the pressure due to the column of air (10 cm) plus the pressure due to the column of mercury (5 cm) from the top of the tube.
Since the two ends of the capillary tube are in equilibrium, the pressures at both ends should be the same.
Equating the pressures at the two ends, we have:
P + 15.cm × m.g = P + 10.cm × m.g + 5.cm × m.g
Here, m.g cancels out on both sides, leaving us with:
15.cm = 10.cm + 5.cm
Therefore, the atmospheric pressure during the experiment is the same as the pressure due to the column of air, which is 5 cm.
Keep in mind that this calculation assumes that the density of the air column remains constant and neglects any other factors that may affect the measurement.