A circular disc D₁ of mass M and radius R has two identical discs D₂ and D₃ of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO', passing through the centre of D₁ , as shown in the figure, will be

Step-by-step solution

Moment of inertia of disc D₁ about O O^ =I₁= M R² 2 M.O.I of D ₂ about OO ^ =I₂= 1 2 ( M R² 2 )+M R²= M R² 4 +M R² M.O.I of D ₃ about OO ^ =I₃= 1 2 ( M R² 2 )+M R²= M R² 4 +M R² so, resultant M.O.I about OO ^ is I = I ₁+ I ₂+ I ₃ aligned & I= M R² 2 +2 ( M R² 4 +M R² ) &= M R² 2 + M R² 2 +2 M R²=3 M R² aligned