Linear Mass Density - Bars (Center of Mass)

[azukibean]

1. Homework Statement
The 4 black bars have constant linear density. In terms of L, find the coordinate of the center of mass

Homework Equations

M0 X = summation of (MiXi)

The Attempt at a Solution

I understand most of the solution, except the answer key says one thing I don't get
M/sqrt(2) at (L/4, L/4)
and at (L/4, 3L/4).
Why is there less mass in the middle of bar though the bar is uniform?

 

[Chestermiller]

M is the mass of a bar of length L. The diagonal of the square is L√2. Half the diagonal is L/√2. That's the length of each of the smaller little bars along the diagonals. So their masses must be M/√2.

Chet

 

[azukibean]

Thanks! That made a lot of sense.