Question

The moment of inertia of an elliptical disc of uniform mass distribution of mass 'm', semi major axis 'r', semi minor axis 'd' about its axis is

• A. $=\frac{m{r}^2}{2}$
• B. $=\frac{m{d}^2}{2}$
• C. $>\frac{m{r}^2}{2}$
• D. $<\frac{m{r}^2}{2}$

Answer 1

The correct option is D $<\frac{m{r}^2}{2}$

we know that the moment of inertia of an circlar disc of uniform mass distribution of mass 'm', radius 'r' about its axis is $\frac{m{r}^2}{2}$

Since, For an elliptical disc of uniform mass distribution of mass 'm', semi major axis 'r', mass distribution is closer to axis so its moment of inertia will be less than $\frac{m{r}^2}{2}$.

Therefore, D is correct option.