Gravitational Force in a Sphere with a Cavity

Question

A small spherical cavity with a radius of $$R/4$$ is created within a uniform sphere of radius $$R$$ and density $$\rho$$. The center of the cavity is located at a distance of $$R/2$$ from the center of the larger sphere. If a particle of mass $$m$$ is placed at the center of the cavity, what is the magnitude of the gravitational force exerted on the particle?

Accepted Answer

$$\frac{4}{3}\pi G \rho m \cdot \frac{R}{2}$$

Answer

$$\frac{4}{3}\pi G \rho m R$$

Answer

$$0$$

Answer

$$\frac{4}{3}\pi G \rho m (R/2)^2$$

Gravitational Force in a Sphere with a Cavity

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