A uniform sphere has a mass M and radius R. Find the pressure p inside the sphere, caused by gravitational compression, as a function of the distance r from its centre. Evaluate p at the centre of the Earth, assuming it to be a uniform sphere.

Explanation

To find the pressure \( p \) inside a uniform sphere as a function of the distance \( r \) from its center, we will follow these steps:

### Step 1: Determine the Density of the Sphere
The density \( \rho \) of the sphere can be calculated using the formula:
\[ \rho = \frac{M}{\frac{4}{3} \pi R^3} \]
where \( M \) is the mass of the sphere and \( R \) is its radius.
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