A spherical body of radius R consists of a fluid of uniform density and is in hydrostatic equilibrium under its own gravity. If P(r) is the pressure at radius r < R, select the correct statement(s).
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Question

A spherical body of radius R consists of a fluid of uniform density and is in hydrostatic equilibrium under its own gravity. If P(r) is the pressure at radius r < R, select the correct statement(s).

G1 Physics · Accepted Answer

Step 1: For a uniform-density self-gravitating fluid sphere, g(r)=(4πGρ/3)r. Hydrostatic equilibrium dP/dr=-ρg givₑ P(r)=(2πGρ²/3)(R²-r²). Step 2: Hence P(3R/4)/P(2R/3)=(1-9/16)/(1-4/9)=63/80, so B is true. Also P(3R/5)/P(2R/5)=(1-9/25)/(1-4/25)=16/21, so C is true. Step 3: P(0) is maximum, not zero, and P(R/2)/P(R/3)=( 3 4 \frac{3}{4} 4 3 ​ )/(8/9)=27/32≠20/27. Final: B and C.

A spherical body of radius R consists of a fluid of uniform density and is in hydrostatic equilibrium under its own gravity. If P(r) is the pressure at radius r &lt; R, select the correct statement(s).

A spherical body of radius R consists of a fluid of uniform density and is in hydrostatic equilibrium under its own gravity. If P(r) is the pressure at radius r < R, select the correct statement(s).