Question

The spaceship S. Lem lands on Solaris (mass 4.04x10²⁴ kg, radius 7.27x10⁷ m, air pressure 1.22x10⁵Pascal). The crew discovers pools of a mysterious substance of specific gravity 13.5. Find the pressure at the bottom of one pool of this substance, 90.9 m deep, in Pascals. Express your answer in scientific notation.

Answer 1

Gravitational constant = G = 6.67 x 10^-11 N.m²/kg²

Mass of the planet Solaris = M = 4.04 x 10²⁴ kg

Radius of the planet Solaris = R = 7.27 x 10⁷ m

Gravitational acceleration on the surface of the planet Solaris = g

g = 0.051 m/s²

Air pressure on Solaris = P₀ = 1.22 x 10⁵ Pa

Density of water = ₀ = 1000 kg/m³

Specific gravity of the mysterious substance = s = 13.5

Density of the mysterious substance =

= 13500 kg/m³

Depth of the pool = H = 90.9 m

Pressure at the bottom of the pool = P

P = 1.846 x 10⁵ Pa

Pressure at the bottom of the pool = 1.846 x 10⁵ Pa