$5$ particles,each of mass $2 \ kg$,are attached to the rim of a circular disc of radius $0.1 \ m$ and negligible mass. The moment of inertia of this system about an axis passing through the center and perpendicular to its plane is ........... $kg \cdot m^{2}$.

$A$ circular disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :

Define moment of inertia,write its unit and dimensional formula.

In a rectangle $ABCD$ where $BC = 2AB$,the moment of inertia will be minimum about which axis?

Four masses are attached to a light circular frame of radius $a$ as shown in the figure. The radius of gyration of this system about an axis passing through the center $O$ of the circular frame and perpendicular to its plane is:

Point masses $1, 2, 3$ and $4 \text{ kg}$ are located at the points $(0,0,0), (2,0,0), (0,3,0)$ and $(-2,-2,0)$ respectively. The moment of inertia of this system about the $x$-axis will be: (in $\text{ kg m}^2$)