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deekin
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Homework Statement
Mass M is distributed uniformly over a disk of radius a. Find the gravitational force between this disk-shaped mass and a particle with mass m located a distance x above the center of the disk.
Homework Equations
The problem gives the hint to use the equation found in an earlier problem for the force of gravity between a ring and a particle. This equation is [itex]\frac{GmMx}{(x^2+a^2)^{3/2}}[/itex] where a is the radius of the ring and x is the distance of the particle with mass m from the ring of mass M.
The Attempt at a Solution
I switched out r (for the radius) for a, integrated with respect to r, and used 0 to a as my limits of integration. [itex]\int \frac{GmMx}{(x^2+r^2)^{3/2}}dr[/itex] I'm not sure how to get the limits of integration on there. Anyway, the answer I got was [itex]\frac{GmMa}{\sqrt{x^2+a^2}}[/itex].
The back of the book has [itex]\frac{2GMm}{a^2}(1-\frac{x}{\sqrt{a^2+x^2}})[/itex]. I'm not sure what I'm doing wrong here. The radius of the ring is what is changing, which is why I integrated with respect to the radius r. Your help would be much appreciated.