On planet X the absolute pressure at a depth of 200 m below

On planet X, the absolute pressure at a depth of 2.00 m below the surface of a liquid nitrogen lake is 5.00 times 10^5 N/m^2. At a depth 5.00 m below the surface, the absolute pressure is 8.00 times 10^5 N/m^2. The density of liquid nitrogen is 808 kg/m^3. What is the atmospheric pressure on planet X? What is the acceleration due to gravity on planet X?

Solution

Here ,

density of N2 , p = 808 Kg/m^3

pressure , P1 = 5 *10^5 Pa , h1 = 2 m

P2 = 8 *10^5 Pa , h2 = 5

a) let the atmospheric pressure is Po

and accleration due to gravity is g

as P = Po + p * g * h

5 *10^5 = Po + 808 * g * 2 ----(1)

8 *10^5 = Po + 808 * g * 5 ----(2)

solving 1 and 2

Po = 3 *10^5 Pa

g = 123.8 m/s^2

the atmospheric pressure on the planet is 3 *10^5 Pa

b)

the acceleration due to gravity is 123.8 m/s^2