An astronaut landed on a far away planet that has a sea of water. To determine the gravitational acceleration on the planet's surface, the astronaut lowered a pressure gauge into the sea to a depth of 28.6 m. If the gauge pressure is measured to be 2.4 atm, what is the gravitational acceleration on the planet's surface?

Respuesta :

The concept required to solve this problem is hydrostatic pressure. From the theory and assuming that the density of water on that planet is equal to that of the earth [tex](1000kg / m ^ 3)[/tex]we can mathematically define the pressure as

[tex]P = \rho g h[/tex]

Where,

[tex]\rho[/tex] = Density

h = Height

g = Gravitational acceleration

Rearranging the equation based on gravity

[tex]g = \frac{P_h}{\rho h}[/tex]

The mathematical problem gives us values such as:

[tex]P = 2.4 atm (\frac{101325Pa}{1atm}) = 243180Pa[/tex]

[tex]\rho = 1000kg/m^3[/tex]

[tex]h = 28.6m[/tex]

Replacing we have,

[tex]g = \frac{243180}{(1000)(28.6)}[/tex]

[tex]g = 8.5m/s^2[/tex]

Therefore the gravitational acceleration on the planet's surface is [tex]8.5m/s^2[/tex]