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Question

A circular disc of radius 1 m is rotating about an axis passing through its COM and perpendicular to its plane. The moment of inertia about this axis is given by Icom=2 kg-m2. If the disc is rotated about an axis along its diameter, then the moment of inertia along that axis is Idia. The value of (IcomIdia) is equal to


A
2 kg-m2
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B
1 kg-m2
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C
3 kg-m2
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D
0.5 kg-m2
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Solution

The correct option is B 1 kg-m2
Given, radius of disc (r) = 1 m
Moment of inertia about axis passing through COM and perpendicular to the plane of the disc, Icom=2 kg-m2
From definition, Icom=Mr22
We get,

M=2Icomr2=2×2(1)2=4 kg
Therefore , Idia=Mr24=4×(1)24
= 1 kg-m2

Hence, IcomIdia=21=1 kg-m2

Method 2:
Idia=Icom2 (from Perpendicular Axis Theorem)
IcomIdia=Icom2=1 kg-m2

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