Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centre form an equilateral triangle of side of length d. The ratio $$I0/IA$$ of moment of inertia $$I0$$ of the system about an axis passing the centroid and about centre of any of the spheres IA and perpendicular to the plane of the triangle is :

Question

Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centre form an equilateral triangle of side of length d. The ratio  $$I0/IA$$ of moment of inertia  $$I0$$ of the system about an axis passing the centroid and about centre of any of the spheres  IA and perpendicular to the plane of the triangle is :

Infinity Learn · Accepted Answer

MOI about centroid  $$=325md22+md32=1310md2$$        [here $$OA=OB=OC=d3$$]MOI about axis passing through ‘r’ and ⊥lr to $$plane=225md22+md2+25md22=2310$$  $$md2$$        ∴  $$Ratio=1323$$

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