Gauss's Law states that the gravatational flux crossing a closed surface is -4piGM, where M is the mass inside the surface.
A Long straight cylinder has a radius R and is made of material of a constant density of p
Show that the gravatational field at a distance r from the axis of the cylinder is proportional to r, for r<R.
f.da = (closed integral) -4piGM
The Attempt at a Solution
I enclosed the cylinder in a Gaussian surface
Mass Enclosed is pi(r)^2lp
f is constant therefore, f.da = f.2(pi)rl
So by gauss's law:
f.2(pi)rl = -4piG[pi(r)^2lp]
So f = -2G(pi)pr.
The problem is when i compare with people they get f = -G(pi)pr.
Is this correct? Either shows that f proportional to r. But the constant 2 is confusing me, should it be there or not?
Any help would be greatly appreciated