A cylindrical drinking glass with diameter 8.6 cm and height 25 cm is inverted and carefully lowered into a tank of water.If no air is allowed to escape from the glass as it is submerged,what is the height of the air column in the glass when the glass is 2.0 m below the surface of the water?

Question

Quizplus · Accepted Answer

The pressure at 2.0 m below the surface can be calculated using the formula $P = P_0 + \rho gh$, where $P_0$ is the atmospheric pressure, $\rho$ is the density of water (1000 kg/m³), $g$ is the acceleration due to gravity (9.8 m/s²), and $h$ is the depth (2.0 m). The pressure inside the glass must equal the pressure outside for no air to escape. Initially, the volume of air is the volume of the cylinder, and finally, it's the volume of a smaller cylinder with the same diameter but unknown height. Using Boyle's Law, $P_1V_1 = P_2V_2$, and knowing the initial and final pressures and the initial volume, we can solve for the final volume and thus the height of the air column. Given the diameter (8.6 cm), we can find the radius (4.3 cm) and use it to calculate the initial volume. The final pressure is the sum of atmospheric pressure and the pressure due to the water column above the glass. With these values, we can find the final volume and thus the height of the air column, which is 20.9 cm.

A Cylindrical Drinking Glass with Diameter 8