Setting up integral for a one-dimensional planet

[musicmar]

Homework Statement

A uniform rod of mass M and length L lies along the x-axis with its center at the origin. Determine the gravitational field at the point x=d where d>L/2.

Homework Equations

The Attempt at a Solution

I know I will have to take the integral of dg in order to find g. g=Gdm/r².

It has uniform density, so λ=M/L

So, dm=(M/L)dr

Now, the problem is finding r.

I called the distance from the origin to the point: d, and the distance from the end of the rod to the point: x. Is r=d? And then you integrate from (-L/2) to (L/2)?

Thank you.

 

[G01]

Draw a picture of your rod. Now mark off the little mass segment, dm.

r is the distance from dm to the point at which you want to calculate the field.

 

[musicmar]

I did that, and I've figured it out. r is r, and you integrate from d-L/2 to d+L/2

 

[G01]

I did that, and I've figured it out. r is r, and you integrate from d-L/2 to d+L/2

Cool!