Grade 12Mechanics
how will you calculate the pressure inside a planet of fluid at a distance r from centre. .
how will you calculate the pressure inside a planet of fluid at a distance r from centre. .
1 Answer
Naveen Balaji
Since since the planet is of a sperical shape, let’s say the radius of the planet is R. Now assume an elemental strip( in 2d it appears as a circle in 3D it's a hollow sphere) or width dr at a distance r from the centre. Now by law of fluid pressure we know that the lower part of the strip experiences a pressure p and the upper portion experiences a pressure p+dp due the fluid above it. Now to find dp: ∫dp = ρgr, now ρ(rho) is the density which is equal to the volume multiplied by the mass of the enclosed portion. V=(4πr³)/3 and you can find the enclosed mass by comparing: M/(4πR³/3) = m/4πr²dr, so m= 3Mr²dr/R³. Now substitute this in the pressure equation to get
p = 4πMg∫r³dr limits from 0 to R. Finally.
p = MgπR³.
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