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

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Infinity Learn · Accepted Answer

Net moment of inertia of the system, $$I=I1+I2+I3$$ The moment of inertia of a shell about its diameter, $$I1=23mr2The$$ moment of inertia of a shell about its tangent is given $$byI2=I3=I1+mr2=23mr2+mr2=53mr2$$∴  $$I=2$$×$$53mr2+23mr2=12mr23=4mr2$$

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

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