Answer :
The moment of inertia of the assembly about the axis perpendicular to the page and passing through point O is 0.285 kg/m².
The dimensions of the block are 300mm x 400mm, the radius of the semi cylinder is 200mm.
The mass of the block is 3 kg and the semi cylinder has a mass of 5 kg.
The Moment of inertia of the block around the axis passing through the point O and perpendicular to the plane of the paper is given by,
I = M/12(L²+B²)
I₁ = M/12((0.3)²+(0.4)²)
I₁ = M/12
I₁ = 0.06 kg/m²
Now, the moment inertia of the semi cylinder around the point O is,
I₂ = M/2(R)²
I₂ = 5/2(0.3)²
I₂ = 0.225 kg/m².
The moment of inertia of the whole assembly around the axis perpendicular to the page and passing through point O.
I = I₁ + I₂
I = 0.06+0.225
I = 0.285 kg/m².
The moment of inertia of the assembly is 0.285 kg/m².
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