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Question

If $$I$$ is the moment of inertia of a thin circular plate about an axis passing through tangent of plate in its plane. The moment of inertia of same circular plate about an axis perpendicular to its plane and passing through its centre is:


A
4I5
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B
2I5
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C
4I3
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D
2I3
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Solution

The correct option is C $$\dfrac{2I}{5}$$
Moment of Inertia of a circular plate about any diameter is $$\frac{MR^2}{4}$$
$$\therefore$$ By parallel axis theorem,across any diameter
      $$I=\frac{MR^2}{4}+MR^2=\frac{5MR^2}{4}$$
Moment of Inertia of a circular plate passing through its centre and perpendicular to its axis is $$\frac{MR^2}{2}$$
       $$=\left (\frac{5MR^2}{4}  \right )\frac{2}{5}=\frac{2I}{5}$$

Physics

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