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Question

Two discs of mass 2 kg and 3 kg of radius 1 m and 2 m respectively placed together are rotated about an axis through their common centre as shown in figure. Find the net moment of inertia of the system about given axis.

A
6 kg-m2
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B
5 kg-m2
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C
1 kg-m2
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D
7 kg-m2
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Solution

The correct option is D 7 kg-m2
Given:
Mass of disc 1, m1=2 kg having radius r1=1 m
Mass of disc 2, m2=3 kg having radius r2=2 m.
Moment of inertia of disc of mass 2 kg I1=m1r212
=2×122=1 kg-m2

Moment of inertia of disc of mass 3 kg,
I2=m2r222
=3×222=6 kg-m2

Net moment of inertia of both discs about given axis
Inet=I1+I2 =(1+6) kg-m2
=7 kg-m2

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