Question

$I$ is moment of inertia of a uniform circular plate about an axis passing through any diameter of plate. The moment of inertia of same plate about an axis perpendicular to the plane of plate and passing through exact midpoint between centre and edge of the plate is:

• A. $\frac{3}{2}I$
• B. $2I$
• C. $3I$
• D. $\frac{5}{4}I$

Answer 1

The correct option is C $3I$

Moment of inertia of a uniform circular plate about an axis passing through any diameter of plate $I=\frac{M{r}^2}{4}$

Moment of inertia of a uniform circular plate about an axis passing through center and perpendicular to plane $I_{cm}=\frac{M{r}^2}{2}$

midpoint between center and edge of the plate is d=r/2

Using parallel axis theorem $I_1=I_{cm}+M{d}^2=\frac{3M{r}^2}{4}$

So $I_1=3I$