Q.

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 :

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a

2313

b

1323

c

1315

d

1513

answer is B.

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Detailed Solution

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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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 :