Point masses $1, 2, 3$ and $4 \text{ kg}$ are lying 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:

Two rods each of mass $m$ and length $\ell$ are joined at their centers to form a cross. What is the moment of inertia of the cross about an axis passing through the common center and perpendicular to the plane formed by them?

$A$ circular disc of radius $10 \ cm$ and thickness $5 \ mm$ has a uniform density of $8 \ g/cc$. Find the moment of inertia of the disc about an axis passing through its center and perpendicular to its plane.

If the diameter of a flywheel is increased by $1\%$,then the percentage increase in its moment of inertia about an axis passing through its center will be ....... $\%$

The moments of inertia of a non-uniform circular disc (of mass $M$ and radius $R$) about four mutually perpendicular tangents $AB, BC, CD, DA$ are $I_1, I_2, I_3$ and $I_4$,respectively (the square $ABCD$ circumscribes the circle). The distance of the centre of mass of the disc from its geometrical centre is given by

Consider a sphere of mass $M$ and radius $R$ centered at the origin. The density of the material of the sphere is $\rho = A r^\alpha$,where $r$ is the radial distance,and $\alpha$ and $A$ are constants. If the moment of inertia of the sphere about the axis passing through the centre is $\frac{6}{7} M R^2$,then the value of $\alpha$ is