A solid sphere of mass M and radius a is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at a distance 3a from the centre will be

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(4) (GM)/(3a²). The shell runs from a out to 3a, so the point asked about sits right on its outer surface and everything is inside. For a point outside, both the sphere and the shell pull as if their mass sat at the centre. Enclosed mass is M+2M=3M. E=(G(3M))/((3a)²)=(GM)/(3a²).

A solid sphere of mass M and radius a is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at a distance 3a from the centre will be

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