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Question

Two spherical balls A and B are connected by the massless rod. The masses of ball A and B are 2 kg and 5 kg. Find the moment of inertia of the system about the axis passing perpendicular to the length of rod as shown in figure bellow.


A
10 kg-m2
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B
18 kg-m2
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C
23 kg-m2
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D
20 kg-m2
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Solution

The correct option is C 23 kg-m2
Given:
mass of ball A;mA=2 kg
Distance of ball A from axis of rotation rA=3 m
Mass of ball B,mB=5 kg
Distance of ball B from axis of rotation rB=1 m

Let IA= moment of inertia of ball A
IB= moment of inertia of ball B
So, total moment of inertia of the system I=IA+IB

I=mAr2A+mBr2B

=2×32+5×12
=23 kg-m2

So, moment of inertia of system is 23 kg-m2

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