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Q.
A thin circular disk is in the $xy$ plane as shown in the figure. The ratio of its moment of inertia about $z$ and $z'$ axes will be :
JEE MainJEE Main 2018System of Particles and Rotational Motion
Solution:
The moment of inertia of a disc about central axis is
$I_{c}=\frac{1}{2} M R^{2}$...(1)
From theorem of parallel axis, we have
$I=I_{ c }+m d^{2}$
$I=\frac{1}{2} M R^{2}+M R^{2} \,\,d=R$
$I=\frac{3}{2} M R^{2}$...(2)
Eq. (1) by (2), we get
$\frac{I_{ c }}{I}=\frac{(1 / 2) M R^{2}}{(5 / 2) M R^{2}}=\frac{1}{3}=1: 3$
