Two identical hollow spheres of mass M and radius R are joined together and the combination is rotated about an axis tangential to one sphere and perpendicular to the line connecting their centres. The moment of inertia of the combination is : 

(34 / 3) MR²

Moment of Inertia of combination : \(I_1 + I_2\)

For sphere (1), from parallel axis theorem : I₁ = I_CM + MR² 

For sphere (2), from parallel axis theorem : I₂ = I_CM + M(R + 2R)² 

hence, I = 2I_CM + MR² +M(3R)² 

I = [(2/5) MR]²(2) + 10MR² 

   = (4/5) MR² + 10MR² 

   = 10.8MR² 

   ≈ (34 / 3) MR²