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- Given a cylinder with constant density, and a mass at one of its ends, it would seem via GmM/r^2) that the gravitational force between the cylinder and the mass would be less than that between the mass and the half of the cylinder closest to the mass, which is absurd, so what is wrong?

Given a cylinder of height 2k with constant density and total mass M, and another object (for simplicity, a point mass) with mass m on the top of the cylinder; the force of gravitation is calculated between the centers of mass, which for the cylinder is at a distance k from the point mass, giving a total force of GmM/k^2. Now however consider the force between the top half of the cylinder and the point mass. The center of gravity of the top half is now k/2 from the point mass, and the mass of the top half is M/2. So the force is now Gm(M/2)/(k/2)^2= 2GmM/k^2, or twice the force with the whole cylinder. That the whole gravitational force should be less than that from half of the cylinder seems to me wrong, but obviously I am some elementary piont. I would be grateful for someone to point out my mistake. Thanks.