A thin disk of radius \(R\) has mass \(m_{\text {disk }}\) uniformly distributed over its area.

(a) Derive an expression for the magnitude of the gravitational force this disk exerts on a particle of mass \(m_{\text {part }}\) located a distance \(y\) directly above the center of the disk.

(b) If \(y \gg R\), show that this expression reduces to that for two particles.