Gravitational Force Between Two Identical Rods of Mass m and Length l

[peeyush_ali]

There are 2 identical rods of mass "m" and length "l" separated by a distance "l" in such a way that the 2 rods are in a straight line. Find the Gravitational force between these two rods.

Homework Equations

The Attempt at a Solution

I'm unable to analyse a calculus based strategy such as chosing the small elemnt of mass "dm" length "dx" and so on..

 

[berkeman]

There are 2 identical rods of mass "m" and length "l" separated by a distance "l" in such a way that the 2 rods are in a straight line. Find the Gravitational force between these two rods.

Homework Equations

The Attempt at a Solution

I'm unable to analyse a calculus based strategy such as chosing the small elemnt of mass "dm" length "dx" and so on..

Just use their centers of mass, and the gravitational force equation. Write that out for us.

 

[peeyush_ali]

so u mean to say that the interaction is nothing but...


F= Gm.m/4 l.l ??

 

[berkeman]

so u mean to say that the interaction is nothing but...


F= Gm.m/4 l.l ??

Almost. What is the separation of the centers of mass in terms of l?

 

[peeyush_ali]

the situation is like this :

|<___________________>|
_____l_____ (l+l/2+l/2) _____l_____ the separation between the centres of the 2 rods is l+l/2 +l/2 =2l

 

[berkeman]

the situation is like this :

|<___________________>|
_____l_____ (l+l/2+l/2) _____l_____


the separation between the centres of the 2 rods is l+l/2 +l/2 =2l

Two rods of length L have their centers of mass separated by L/2 or 2L? Why? Not.

 

[peeyush_ali]

the centres are separated by a length of 2l

 

[berkeman]

the centres are separated by a length of 2l

If each rod is length L, then I don't think so. Just use a practical example. What if each rod is 1 meter long, and you stack them end-to-end. How far apart are the centers of the rods?