Four holes of radius R are cut from a thin square plate of side 4 R and mass M . The moment of inertia of the remaining portion about z -axis is

Step-by-step solution

I remaining = I total - I removed I remaining = I total - 4 I each   disc I remaining = I = I total - 4 × ( I disc + M disc 2 R 2 ) (From parallel axis theorem) I = 1 12 M 32 R 2 - 4 × 1 2 × πM 16 × R 2 + πM 16 × 2 R 2 ∵ M disc = πM 16 I = 8 3 MR 2 - 4 × 5 2 × πM 16 × R 2 = MR 2 8 3 - 20 π 32 I = 8 3 - 10 π 16 M R 2