Derive Gravitational Force and Field between two identical rods

[RIJU101]

Homework Statement

What is the Gravitational force and field between two identical rods(radius of cross-section is R) of uniform density, which are placed parallel to each other? Derive the formula for two cases:

1.When two rods are finite in length
2.When two rods are of infinite length

Relevant Equations

Gravitational Force: F=GMm/r^2
Gravitational Field: I=GM/r^2

Maybe it can be done by considering both rods as many small elemental masses then deriving the force we can integrate it

 

[haruspex]

Maybe it can be done by considering both rods as many small elemental masses then deriving the force we can integrate it

So try that and post your attempt.