Question

On planet X, the absolute pressure at a depth of 2.00 m below the surface of a liquid nitrogen lake is 5.00 × 105 N/m2 . At a depth 5.00 m below the surface, the absolute pressure is 8.00 × 105 N/m2 . The density of liquid nitrogen is 808 kg/m3 . a. What is the atmospheric pressure on planet X? b. What is the acceleration due to gravity on planet X?

Answer 1

Answer:

300000.01008 Pa

123.76237 m/s²

Explanation:

$\rho$ = Density of liquid nitrogen = 808 kg/m³

h = Depth

g = Acceleration due to gravity

P = Atmospheric pressure

Absolute Pressure is given by

Below 2 m from surface

$P_a=P+\rho gh\\\Rightarrow 5\times 10^5=P+808g\times 2$

Below 5 m from surface

$P_a=P+\rho gh\\\Rightarrow 8\times 10^5=P+808g\times 5$

Subtracting the above equations we get

$-3\times 10^5=-808g3\\\Rightarrow g=\frac{3\times 10^5}{808\times 3}\\\Rightarrow g=123.76237\ m/s^2$

The acceleration due to gravity on the planet is 123.76237 m/s²

Equating the value of g in the first equation

$5\times 10^5=P+808\times 123.76237\times 2\\\Rightarrow P=5\times 10^5-808\times 123.76237\times 2\\\Rightarrow P=300000.01008\ Pa$

The atmospheric pressure on the planet is 300000.01008 Pa