First slide
Moment of intertia
Question

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

Moderate
Solution

The situation is shown in fig 

The moment of inertia of each of spheres A and D about AD
=25Ma2
The 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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