Calculating pressure inside a solid sphere
Classical Mechanics
Level
3
A uniform solid sphere has mass \(M\) and radius \(R\). The pressure \(P\) inside the sphere caused by gravitational compression as a function of distance \(r\) from the center of the sphere is given by \[ P(r) = \dfrac ab \cdot \dfrac{GM^2}{\pi R^4} \left( 1 - \dfrac{r^2}{R^2} \right), \] where \(a\) and \(b\) are coprime positive integers.
Find the value of \(a+b\).
Notation: \(G\) denotes the universal gravitational constant: \(G = \SI[per-mode=symbol]{6.67e-11}{\newton\meter\squared\per\kilogram\squared}\).
by
Tapas Mazumdar