A particle of mass `m` is situated at a distance `d` from one end of a rod of mass `M` and length `L` as shown in diagram. Find the magnitude of the gravitational force between them

Explanation

consider an elementof mass 'dm' and length 'dx' at a distance 'x' from the point mass. Mass of the element `dm=M/L dx`.
Gravitational force on 'm' due to this elements is `dF=(Gm(M/L dx))/(x^(2)), F=int_(d)^((d+L))(Gm(M/L)dx)/(x^(2))`
`rArr F=(GmM)/Lint_(d)^((d+L))x^(-2)dx=(GmM)/L[(x^(-1))/(-1)]_(d)^((d+L))`
`rArr F=(GmM)/L[(-1)/x]_(d)^((d+L))=(GmM)/L[1/d-1/((d+L))]`
`F=(GmM)/L[(d+L-d)/((d+L)d)]=(GmM)/(a(a+L))`