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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a
165mr2
b
4mr2
c
115mr2
d
3mr2
answer is B.
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Detailed Solution
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