Consider an infinitesimally thin circular disk of radius \( R \) and mass \( M \) centered at the origin sitting in the \( xy \)-plane. The disk has non-uniform surface mass density \( \sigma \) which varies linearly with radius, i.e., \( \sigma = cr \). **(b)** Determine the gravitational field \( \mathbf{g}(r) \) at the point \((0, 0, z)\) above the disk.**(c)** Determine the gravitational potential \( \Phi(r) \) at the point \((0, 0, z)\) above the disk.

(b) Consider a small element on the disk. The mass element be calculated as,…

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Consider an infinitesimally thin circular disk of radius R and mass M centered at the origin sitting in the xy-plane. The disk has non-uniform surface mass density o which varies linearly with radius, i.e., o = cr.