If we assume that the mass density, \(\rho\), of the object is constant (the body is made of a uniform material), then the density is simply the mass of the object over its volume: \[\begin{aligned} \...If we assume that the mass density, \(\rho\), of the object is constant (the body is made of a uniform material), then the density is simply the mass of the object over its volume: \[\begin{aligned} \rho = \frac{M}{\frac{4}{3}\pi R^3}\end{aligned}\] The amount of mass enclosed by the spherical surface of radius \(r\) is the density multiplied by the volume of a sphere of radius \(r\): \[\begin{aligned} M^{enc} = \rho \frac{4}{3}\pi r^3 = M\frac{r^3}{R^3}\end{aligned}\] Applying Gauss’ Law, we c…
