Astronauts visiting a new planet find a lake filled with an unknown liquid. they have with them a plastic cube, 8.0 cm on each side, with a density of 840 kg/m3. first they weigh the cube with a spring scale, measuring a weight of 25 n. then they float the cube in the lake and find that two-thirds of the cube is submerged. at what depth in the lake will the pressure be twice the atmospheric pressure of 85 kpa?

depth is 1.16 m

Explanation:

given data

length = 8 cm

density = 840 kg/m³

weight = 25 N

atmospheric pressure = 85 kPa

to find out

what depth in the lake will the pressure be twice the atmospheric pressure

solution

we know here that two thirds of the cube is submerged

we get first mass of cube that is

mass = 0.08³ × 0.08 = 0.43008 kg

and g = weight ÷ mass

g =

g = 58.12 m/s²

and we get now ρ for two thirds of the cube is submerged that is

weight = 0.08³ × 58.12 × ρ ×

25 = 0.08³ × 58.12 × ρ ×

ρ = 1260.18 kg/m³

pressure = ρgd   ..................1

pressure = 1260.18 × 58.12 × d

85 × 10³ = 1260.18 × 58.12 × d

d = 1.16 m

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