Question

Moment of a inertia of a sphere about its diameter is $2/5M{R}^2$. What its moment of inertia about an axis perpendicular to its two diameter and passing through their point of intersection.?

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

Answer 1

The correct option is A $I=\frac{2}{5}M{r}^2$

moment of inertia of sphere about its diameter:$I=\frac{2M{R}^2}{5}$

two diameter always inetersect at the centre.

however,a sphere in symmetric from all directions,

so taking any other diameter axis will have moment,

$I=\frac{2}{5}M{R}^2$ (i.e. same)