Question

A uniform disc of radius $R$ lies in the $x-y$ plane, with its centre at origin. Its moment of inertia about $z$ -axis is equal to its moment of inertia about line $y=x+c$. The value of $c$ will be

• A. $-\frac{R}{2}$
• B. $\pm \frac{R}{\sqrt{2}}$
• C. $\frac{+R}{4}$
• D. -R

Answer 1

Answer: (B)

$I_{PQR}=I_{AOB}+M\cdot (ON{)}^2{I}_{PQR}$
$=\frac{1}{4}M{R}^2+M\cdot {\left(\frac{c}{\sqrt{2}}\right)}^2$

But $I_{PQR}=\frac{1}{2}M{R}^2$
$\therefore c=\pm \frac{R}{\sqrt{2}}$