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Q.

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

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a

45Ma2+2Mb2

b

85Ma2+2Mb2

c

85Ma2

d

45Ma2+4Mb2

answer is B.

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Detailed Solution

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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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