MCAT Physics Question 54: Answer and Explanation

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Question: 54

9. A large cylinder is filled with equal volumes of two immiscible fluids. A balloon is submerged in the first fluid; the gauge pressure in the balloon at the deepest point in the first fluid is found to be 3 atm. Next, the balloon is lowered all the way to the bottom of the second fluid, where the hydrostatic pressure in the balloon reads 8 atm. What is the ratio of the gauge pressure accounted for by the first fluid to the gauge pressure accounted for by the second fluid?

  • A. 1:03
  • B. 3:04
  • C. 3:05
  • D. 3:08

Correct Answer: B

Explanation:

The first step in answering this question is defining the different types of pressures. Atmospheric pressure is the pressure at the top of the first fluid exerted by air (at sea level, it is equal to 1 atm). Gauge pressure is the pressure inside the balloon above and beyond atmospheric pressure; gauge pressure is the total (absolute or hydrostatic) pressure inside the balloon minus the atmospheric pressure. Gauge pressure depends on the density of the fluid, the constant of gravity, and the depth at which the object is submerged. Hydrostatic or absolute pressure is the total pressure in the balloon (that is, the gauge pressure and the atmospheric pressure together). Because we are given the gauge pressure at the bottom of the first fluid as 3 atm, our task now is to calculate the gauge pressure accounted for by the second fluid. The hydrostatic pressure at the bottom of the cylinder is 8 atm. One of these atmospheres is atmospheric pressure pushing on the fluids. Another 3 atmospheres are accounted for by the first fluid that is pushing on the second fluid. Thus, the gauge pressure due to the second fluid is 8 ? 1 ? 3 = 4 atm. The ratio of the gauge pressures is therefore 3:4.

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