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Questions  

Four sphere of diameter 2a and mass M are placed with their centres of the four comers of a square of side b. Then the moment of inertia of the system about an axis along one of the sides of the square is

a
45Ma2+2Mb2
b
85Ma2+2Mb2
c
85Ma2
d
45Ma2+4Mb2

detailed solution

Correct option is B

The situation is shown in fig The moment of inertia of each of spheres A and D about AD=25Ma2The moment of inertia of each of spheres I and C about AD=25Ma2+Mb2∴ Moment of inertia of whole arrangement about the side AD is given by=225Ma2+25Ma2+Mb2=85Ma2+2Mb2

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