F=ma 2021 Problem 19

A cavity of radius R / 2 is dug out of a spherical planet with uniform mass density of mass M and radius R. What is the magnitude of the gravitational field at point P in the diagram below?

Answer Choices
A. (0.200) G M / R^{2}
B. (0.457) G M / R^{2}
C. (0.829) G M / R^{2}
D. (0.900) G M / R^{2}
E. (0.912) G M / R^{2} \leftarrow CORRECT