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Question

The moment of inertia of a circular disc of radius $$2m$$ and mass $$1kg$$ about an axis passing through its centre of mass and perpendicular to plane is $$2kg-{m}^{2}$$. Its moment of inertia about an axis parallel to this axis and passing through its edge in $$kg-{m}^{2}$$ is


A
10
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B
8
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C
6
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D
4
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Solution

The correct option is C $$6$$
$$\begin{array}{l} By\, \, applying\, \, the\, \, theorem\, \, of\, \, parallel\, \, axes\, \, moment\, \, of\, \, inertia\, \, 'I'\, \, of\, \, a\, \, body\, \, is\, \, I=Ig+M{ R^{ 2 } } \\ where\, \, Ig\, \, is\, \, the\, \, moment\, \, of\, \, inertia\, \, anout\, \, an\, \, axis\, \, pas\sin  g\, \, through \\ the\, \, centre\, \, of\, \, mass\, \, but\, \, perpendicular\, \, to\, \, the\, \, plane\, \, of\, \, the\, \, body\, \, plus\, \, M{ R^{ 2 } } \\ where\, \, M\, \, is\, the\, \, mass\, \, of\, the\, \, body\, \, and\, \, R\, \, is\, \, the\, \, dis\tan  ce\, \, between\, \, the\, \, axis\, \, and\, \, the\, \, centre\, \, of\, \, mass. \\ I=2+1\times { 2^{ 2 } }=6\, kg{ m^{ 2 } } \end{array}$$
Hence,
option $$(C)$$ is correct answer.

Physics

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