a narrow uniform rod has length $2$a$.$ the linear mass density of the rod is p$,$ so the mass m of a length l of the rod is pl$.$ a$)$ a point mass is located at a perpendicular distance r from the center of the rod. calculate the magnitude and direction of the force that the rod exerts on the point mass. b$)$ what does your result become for a $>>>$ r$?$ c$)$ for a$>>$ r$,$ what is the gravitational field g$=$ Fg$/$m at a distance r from the rod? d$)$ consider a cylinder of radius r and length L whose axis is along the rod. As in part c$,$ let the length of the rod be much greater than both the radius and length of the cylinder. then the gravitational field is constant on the curved side of the cylinder and perpendicular to it$,$ so the gravitational flux through this surface is equal to gA$,$ where A$=2$ pirL is the area of the curved side of the cylinder. calculate this flux. write your result in terms of the mass M of the portion of the rod that is inside the cylindrical surface. How does your result depend on the radius of the cylindrical surface?