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Question

In the system below, the moment of inertia of the combination of thin rod of mass m and solid spherical ball of mass 2m about the axis of rotation AA is:


Your Answer
A
11215mr2
Correct Answer
B
30215mr2
Your Answer
C
31215mr2
Your Answer
D
217mr2

Solution

The correct option is B 30215mr2
Moment of inertia of thin rod about axis AA is, 
Irod=ml23=m(2r)23=4mr23
Moment of inertia of solid spherical ball about an axis passing through its geometrical centre is, I=25(2m)r2=4mr25
Using parallel axis theorem, we get its moment of inertia about axis AA to be,
IAA=4mr25+(2m)(3r)2=4mr25+18mr2=94mr25Itotal=4mr23+94mr25=[20+28215]mr2=302mr215

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