A point mass `M` is at a distance `S` from an infinitely long and thin rod of linear density `D`. If `G` is the gravitational constant then gravitational force between the point mass and the rod is

Options

A. `2(GMD)/S`
B. `(MGD)/S`
C. `(MGD)/(2S)`
D. `2/3(MGD)/S`

Answer

A

Explanation

`dm=Dxxdl=Dxx(Sdalpha)/(cosalpha)`
Gravitational force, `dF=(GMdm)/((S/(cosalpha)))cos alpha` total force `F=int_(-pi//2)^(pi//2)(MGD)/Scos alpha d alpha=(2MGD)/S`