- #1

- 8

- 0

## Homework Statement

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.

## Homework Equations

**f**.d

**a**= (closed integral) -4piGM

## The Attempt at a Solution

I enclosed the cylinder in a Gaussian surface

Mass Enclosed is pi(r)^2l

*p*

f is constant therefore,

**f**.d

**a**= f.2(pi)rl

So by gauss's law:

f.2(pi)rl = -4piG[pi(r)^2l

*p*]

So f = -2G(pi)

*p*r.

The problem is when i compare with people they get f = -G(pi)

*p*r.

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