Question

A thin circular disk is in the $xy$ plane as shown in the figure. The ratio of its moment of inertia about $z$ and $z^{\prime }$ axes will be :

• A. 1 : 3
• B. 1 : 4
• C. 1 : 5
• D. 1 : 2

Answer 1

Answer: (A)

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
$\frac{I_c}{I}=\frac{(1/2)M{R}^2}{(5/2)M{R}^2}=\frac{1}{3}=1:3$