Calculating Gravitational Potential Using Gauss's Law for a Thin Rod

[tatiana_eggs]

Homework Statement

Calculate the gravitational potential due to a thin rod of length l and mass M at a distance R from the center of the rod and in a direction perp. to the rod.

Homework Equations

integral form of Gauss's law wrt gravitation

The Attempt at a Solution

Can I use Gauss's law here i.e. solve for the gravitational field vector and integrate it to get gravitational potential? If not, why?

I tried but I don't get the same answer as with direct integration.

 

[fzero]

Yes, it should be possible to solve that way. You might want to try to show your work in case someone here can spot a mistake.