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The axis $X$ and $Z$ in the plane of a disc are mutually perpendicular and $Y -$ axis is perpendicular to the plane of the disc. If the moment of inertia of the body about $X$ and $Y$ axis is respectively $80 k g m^{2}$ and $100 k g m^{2}$ then moment of inertia about $Z -$ axis will be:

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zero

$180 k g m^{2}$

$20 k g m^{2}$

$40 k g m^{2}$

answer is C.

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Detailed Solution

As disc is lying in the $x - z$ plane, so applying perpendicular axis theorem. $I_{x} + I_{z} = I_{y}$

$80 + I_{z} = 100 \Rightarrow I_{z} = 100 - 80 = 20 k g m^{2}$ .

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