Question

A uniform sphere has a mass M and radius R . Find the gravitational pressure P inside the sphere , as a function of the distance r from its centre

Answer 1

R.E.F image

The solid sphere into This spherical

layers and consider a layer of

Thickness dr lying at a distance 'r'

from center of ball. Each spherical

layer preserve on the layers with init

The considered layer is attracted to the past of sphere lying with it

Hence for considered layer

$dp4\pi r^2=df$

$dp4\pi r^2=\frac{\gamma \left(\frac{4}{3}\pi r^{3}p\right)}{r^2}$ P in mean density of sphere

or $dp=\frac{4}{3}\pi \gamma p^{2}dr$

Then $p=\frac{3}{8}(1-\left(\frac{r^2}{R^2}\right))\gamma m^2/\pi R^4$