Question

Six particles each of mass $5\text{kg}$ are placed along the circumference of a circle of radius $3\text{m}$. What is the moment of inertia of the system about an axis passing through the centre of the circle and perpendicular to the plane of the circle?

• A. $45{\text{kg.m}}^2$
• B. $90{\text{kg.m}}^2$
• C. $270{\text{kg.m}}^2$
• D. $100{\text{kg.m}}^2$

Answer 1

The correct option is C $270{\text{kg.m}}^2$

The particles of mass $m=5\text{kg}$ are placed on the circumference of a circle with $r=3\text{m}$.
$\because$ Moment of inertia of each particle
$=m{r}^2$
$\Rightarrow$Here all the particles are equidistant from the axis of rotation, which is passing through centre of circle and is perpendicular to plane of circle.


Hence moment of inertia of system of $6$ particles is:
$\text{I}=m{r}^2+m{r}^2+m{r}^2+m{r}^2+m{r}^2+m{r}^2$
$\text{I}=6m{r}^2=6\times 5\times 3^2$
$\therefore \text{I}=270{\text{kg.m}}^2$
Hence the correct option is (c).