Two spheres each of mass ' M ' and radius R 2 are connected at the ends of massless rod of length ' 2 R '. What will be the moment of inertia of the system about an axis passing through centre of one of the spheres and perpendicular to the rod?

Step-by-step solution

From parallel axis theorem, I _ o = I _ c + Mh ^2 Let the moment of inertia of sphere 1 be I ₁= 2 5 M ( R 2 )^2+ M (2 R )^2 and, Let the moment of inertia of sphere 2 be I ₂= 2 5 M ( R 2 )^2 Moment of inertia of the rod I ₃=0 Moment of inertia of the system, aligned I & = I ₁+ I ₂+ I ₃ I & = 2 5 M ( R 2 )^2+ M (2 R )^2+ 2 5 M ( R 2 )^2 & = 4 5 M ( R 2 )^2+4 MR ^2 & = 1 5 MR ^2+4 MR ^2 & = 21 5 MR ^2 aligned