I want to calculate the gravitational force between a uniform rod of mass $2\,\rm kg$, length $1\,\rm m$ and a uniform sphere of mass $0.2\,\rm kg$. Distance between the sphere and the rod is $0.1\,\rm m$. The sphere is in the same line as the rod, i.e. sphere is one meter from the near end of the rod.
I thought of integrating
$$\frac{GmM}{x^2}$$
from $0.1$ to $1.1$ meter which does yield the correct result, but the solution in the textbook has a different procedure.
Best Answer
Thank you for your comments. As for the solution in the textbook, they integrated the gravitational field an then calculated the force.