Question

Moment of inertia of a thin circular plate of mass $M$, radius $R$ about an axis passing through its diameter is $I$. The moment of inertia of a circular ring of mass $M$, radius $R$ about an axis perpendicular to its plane and passing through its centre is:

• A. $2I$
• B. $\frac{I}{2}$
• C. $4I$
• D. $\frac{I}{4}$

Answer 1

Answer: (C)

$4I$

We know moment of inertia of a disc ,axis passing through its diameter is $I=m{r}^2/4$

Moment of inertia of ring about its axis passing through diameter $I_1=m{r}^2/2=2I$

Now using perpendicular axis theorem $I_z=I_x+I_y=2I_1=4I$