Question

moment of inertia of a uniform circular disc about a diameter is i. its moment of intertia about an axis perpendicular to its plane and passing through a point on its rim will be: (a) 5I (b) 3I (c) 6I (d) 4I

Answer 1

we know, moment of inertia of a uniform circular disc of mass M and radius R about an axis passing through centre is given by,
$I_{\textbf{centre}}=\frac{1}{2}MR^2$

from perpendicular axis theorem,
moment of inertia of disc about a diameter , $I_{\textbf{diameter}}=\frac{I_{\textbf{centre}}}{2}$

a/c to question, it is given that, moment of inertia of disc about a diameter is I
then, $I=\frac{1}{2}I_{\textbf{centre}}=\frac{1}{4}MR^2$

so, $MR^2=4I$........(1)

now, we have to find moment of inertia about an axis perpendicular to its plane and passing through a point on its rim.
use parallel axis theorem,
$I_{\textbf{rim}}=I_{\textbf{centre}}+MR^2$

$I_{\textbf{rim}}=\frac{1}{2}MR^2+MR^2=\frac{3}{2}MR^2$

so, $I_{\textbf{rim}}=\frac{3}{2}4I=6I$

hence, option (c) is correct.

Answer 2

it's answer is 6I..............