A Remarkable Planet

Q: An interstellar explorer discovers a remarkable planet made entirely of an uniform incompressible liquid of density " ρ ". The radius of the planet is " R " and Accn. due to gravity at surface is " g ".

What is the pressure at the center of the Planet.

13 Answers

71
Vivek @ Born this Way ·

Q: A cubical block of side length " a " and density " ρ " slides over the fixed incline with velocity " v ". There is a thin film of fluid of thickness " t " between plane and block, then find the coefficient of viscosity.

11
Soham Mukherjee ·

Q.1 hope so 0...cos g must be 0..

71
Vivek @ Born this Way ·

if that would have been the answer i wouldn't have posted it. sorry.

1
munadifrekin ·

is the answer to first one 2Pi G rho ^{2} R^{2} / 3

71
Vivek @ Born this Way ·

no

11
sagnik sarkar ·

Hey,I am also getting the same answer.

71
Vivek @ Born this Way ·

Soorry.. Still wrong.!

23
qwerty ·

ρgR/2 ?

71
Vivek @ Born this Way ·

Please post the solution!

23
qwerty ·

go at some x, take a shell (of liquid) of thickness ∂x.

gravitational force on this shell is balanced by the force due to difference in pressure at x and x+∂x

so (Px - Px+dx)4πx2 = GMρ4πx3dxR3

and use Px - Px+dxdx ≈ - dPdx

and integrate both sides for x = 0 to x = R

and Px=0 = P required

Px=R= 0

71
Vivek @ Born this Way ·

gravitational force on this shell is balanced by the force due to difference in pressure at x and x+∂x

Would you mind posting a FBD for that please.

23
qwerty ·

PS : the area dA is the cross sectional area of the cylinders

71
Vivek @ Born this Way ·

Anyways, I finally managed to solve it. Thanks!

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