[Physics] Calculate gravitational force between a sphere and a uniform rod

homework-and-exercisesnewtonian-gravity

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.