Two spheres each of mass M and radius R/2 are connected with a mass less rod of length 2R as shown in figure. What will be moment of inertia of the system about an axis passing through centre of one of the spheres and perpendicular to the rod?

(21 / 5) MR²

Moment of Inertia about yy1 = I

I = (2/5) M(R / 2)² + (2/5) M(R / 2)² + M(2R)² 

as Moment of Inertia of sphere = (2/5)MR²­ 

hence I = (4/5) M ∙ (R² / 4) + 4R²M

  = 4MR²[{1 / (20)} + 1]

  = (21 / 5)MR²