Question

Find the ratio of moment of inertia of a ring and a disc about an axis passing through their center and perpendicular to their plane. Both ring and disc have the same mass and same radius.

• A. $2:1$
• B. $1:4$
• C. $1:2$
• D. $4:1$

Answer 1

The correct option is C $1:2$

Let the mass of the disc and ring $=m$
Let the radius of the disc and ring $=r$

We know, the $MOI$ of a disc about an axis passing through the center and perpendicular to the plane is
$I_1=\frac{m{r}^2}{2}$ ...(I)

and MOI of a ring about an axis passing through the center and perpendicular to the plane is
$I_2=m{r}^2$ ...(II)

From (I) divided by (II) :
$\frac{I_1}{I_2}=\frac{m{r}^2/2}{m{r}^2}=\frac{1}{2}$
$I_1:I_2=1:2$