A solid sphere of uniform density and mass $M$ has radius $4 \mathrm{m}.$ Its centre is at the origin of the coordinate system. Two spheres of radii $1 \mathrm{m}$ are taken out so that their centres are at $P(0,-2,0)$ and $Q(0,2,0),$ respectively. This leaves two spherical cavities. What is the gravitational field at the origin of the coordinate axes?

A solid sphere of uniform density and mass $M$ has radius $4 \mathrm{m}.$ Its centre is at the origin of the coordinate system. Two spheres of radii $1 \mathrm{m}$ are taken out so that their centres are at $P(0,-2,0)$ and $Q(0,2,0),$ respectively. This leaves two spherical cavities. 

A solid sphere of uniform density and mass $M$ has radius $4 \mathrm{m}.$ Its centre is at the origin of the coordinate system. Two spheres of radii $1 \mathrm{m}$ are taken out so that their centres are at $P(0,-2,0)$ and $Q(0,2,0),$ respectively. This leaves two spherical cavities. 

A cavity of radius$\frac{R}{2}$ is made inside a solid sphere of radius $R$. The centre of the cavity is located at a distance $\frac{R}{2}$ from the centre of the sphere. The gravitational force on a particle of mass $m$ at a distance$\frac{R}{2}$ from the centre of the sphere on the line joining both the centres of the sphere and the cavity is (opposite to the centre of cavity). [$\mathrm{Here}, g=\frac{GM}{R^2}$ where $M$ is the mass of the solid sphere.]