A mass `m` is at a distance a from centre of a uniform rod of length `l` and M. The gravitational force on the mass due to the rod is

Explanation

`dF` = force on element in horizontal direction `= (G. dM. m)/((x + a)^(2))`
where `dM = (M)/(l) dx`
`F=intdF=underset(0)overset(l)int(G.Mmdx)/(l(x +a)^(2)) = (G.Mm)/(l)underset(0)overset(l)int(dx)/((x+a)^(2)) = (G.Mm)/(l)[-(1)/((l+a))+(1)/(a)]=(GMm)/((l+a)a)` .