Question on: JAMB Physics - 2023

Calculate the absolute pressure at the bottom of a lake at a depth of 32.8 m. Assume the density of the water is 1 x 10-3 kgm-3 and the air above is at a pressure of 101.3 kPa.

[Take g = 9.8 ms-2]

422.7

220.14

464.53

321.74

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Correct Option: A

To calculate the absolute pressure at the bottom of the lake, we need to consider both the pressure due to the water column above and the atmospheric pressure acting on the water surface.

The formula for pressure due to a fluid column is given by:

P = ρgh

where:

P is the pressure due to the water column,
ρ is the density of water (1 x 10³ kg/m³),
g is the acceleration due to gravity (9.8 m/s²),
h is the depth of the lake (32.8 m).

Substituting the given values:

P = (1 x 10³ kg/m³) * (9.8 m/s²) * (32.8 m) = 321,440 Pa = 321.44 kPa

The atmospheric pressure (P_atm) is given as 101.3 kPa. The absolute pressure (P_abs) is the sum of the pressure due to the water column and the atmospheric pressure:

P_abs = P + P_atm

P_abs = 321.44 kPa + 101.3 kPa = 422.74 kPa

Therefore, the absolute pressure at the bottom of the lake is approximately 422.7 kPa.