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Question:

Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through the diameter of the third shell. Moment of inertia of the system consisting of these three spherical shells about XX' axis is

115mr2

165mr2

4mr2

3mr2

Solution:

Moment of inertia of the top sphere about an axis passing through its center:
Itop=2/3mr2
Using parallel axis theorem, MI of one of the bottom sphere about the axis XX' is
Ibottom=2/3mr2+mr2=5/3mr2
MI of both bottom spheres is
2×Ibottom=10/3mr2
Total MI of the system:
I=2/3mr2+10/3mr2=4mr2