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Question

In the figure shown below, a solid sphere of radius 5 m is arranged concentrically with a hollow sphere of radius 9 m. Find the moment of inertia of the system about an axis passing through their centre. (Take ms= mass of solid sphere =5 kg,mh= mass of hollow sphere =3 kg).


A
202 kg-m2
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B
212 kg-m2
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C
162 kg-m2
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D
81 kg-m2
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Solution

The correct option is B 212 kg-m2
Given, radius of solid sphere (rs)=5 m
Radius of hollow sphere (rh)=9 m
Moment of inertia of solid sphere Is=25msr2s
=25×5×(5)2
=50 kg-m2

Moment of inertia of hollow sphere Ih=23mhr2h
=23×3×(9)2
=162 kg-m2

Total moment of inertia about axis passing through centre
(I)=Is+Ih=212 kg-m2

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