A mass m is at a distance a from one end of a uniform rod of length l and mass M. Find the gravitational force on the mass due to the rod.

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)` .