What is the Moment of Inertia for a Rod?

[coldblood]

Hi friends,
Please help me in solving this problem, I'll appreciate the help.

The problem is as:

https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-ash3/q71/s720x720/1467427_1461727597387679_1141225220_n.jpg

Attempt -

https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-ash3/q71/s720x720/1472752_1461727710721001_1917071548_n.jpg

Thank you all in advance.

 

[haruspex]

You treated the rod furthest from the axis as a point mass at its centre.
Also, I think you have confused the mass per rod with the total mass.

 

[coldblood]

You treated the rod furthest from the axis as a point mass at its centre.
Also, I think you have confused the mass per rod with the total mass.

So what will with the farthest rod Should I take its moment of inertia as ml²/12(about center) + m(l√3/2)²

If I do so,

The total M.I. is found to be (3/2) ml²

Which gives radius of giration as l√(3/2)

But the answer is l/√2

 

[haruspex]

So what will with the farthest rod Should I take its moment of inertia as ml²/12(about center) + m(l√3/2)²

Yes.

If I do so,

The total M.I. is found to be (3/2) ml²

Which gives radius of giration as l√(3/2)

But the answer is l/√2

That's the other error I mentioned. If each rod has mass m then the entire structure has mass 3m. If its radius of gyration is k then its moment of inertia will be 3mk².

 

[coldblood]

Well, I did a mistake in reading the question also. I thought that I have to calculate the moment of inertia of the system about the axis parallel to the plane of the structure.

If I have to find the M.I. of the system about an axis parallel, So what would the M.I of the farthest rod?
In that case should I treat it as a point mass situated at the center of the rod?

 

[haruspex]

Well, I did a mistake in reading the question also. I thought that I have to calculate the moment of inertia of the system about the axis parallel to the plane of the structure.

If I have to find the M.I. of the system about an axis parallel, So what would the M.I of the farthest rod?
In that case should I treat it as a point mass situated at the center of the rod?

Yes.