Posted by hriday on Monday, January 5, 2009 at 1:05pm.
The center of mass is L/3 from mass 2m and 2L/3 from mass m. Add the moment of inertia contributions of each mass to get
m*(2L/3)^2 + (2m)(L/3)^2
= mL^2*(4/9 + 2/9)
= (2/3) mL^2
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