Solution to Mass Center Problem: 3 Uniform Disks

[braindead101]

question:
three uniform disks of the same mass per unit area, and radii a, 2a, 3a are placed in contact with each other with their centers on a straight line. how far is the center of mass of the system from the center of the smallest disk?

solution:
m1=pi a^2
m2=4pi a^2
m3=9pi a^2

Xc = (m1/mtotal)Xo + (m2/mtotal)(Xo+3a)+(m3/mtotal)(Xo+8a)
Xc = 1/14Xo + 4/14Xo + 6/7a + 9/14Xo + 72/14a
Xc = Xo + 6a

therefore center of mass of system is 6a from the center of the smallest disk.

is this correct?

 

[Tide]

No, that is not correct. Think about what your answer means if a is made arbitrarily small. Also, it appears there is missing information in the way you state the problem. Don't you suppose the thickness of the disks matters?

 

[braindead101]

i don't really understand what's wrong with it
but here is the diagram, i guess i did miss this

http://img63.imageshack.us/img63/9140/phys27rv.jpg

 

[Tide]

braindead,

I misunderstood your original description of the arrangement. I had them stacked one on top of the other - thanks for clarifying with your drawing.

With the revised configuration, yes, your answer is correct!