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MCAT Physics Question — Pressure Difference

If the pressure difference measured at two depths of a tank of mercury is 130,000 Pa, what is the height difference between the two depths? (Use specific gravity of mercury = 13 and gravity = 10m/sec2)


A. 10cm

B. 1m

C. 10m

D. 1000m

Click for Explanation

In a column of fluid, the pressure difference between two depths is given by the formula ΔP = (SG)ρwatergh, where ΔP is the pressure difference, SG is the specific gravity of the fluid, and ρwatergh is the product of water density, gravity, and height difference. Remember that specific gravity, SG, is the ratio of fluid density to water density. Water density is 1g/cm3 or 1000kg/m3.

130,000Pa = 13* 1,000kg/m3 * 10 m/sec2 * h, h = 1m.

A. 10cm, incorrect.

B. 1m, correct.

C. 10m, incorrect, This answer neglects the contribution from gravity.

D. 1000m, incorrect, This answer uses 1kg/m3 for the density of water rather than the correct value of 1000kg/m3.

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