A particle is revolving in a circle of radius $r$, having centre at $\mathrm{O}$, with uniform angular velocity$\omega .$

Choose the correct option(s):

A uniform square plate $S$ (side $c$) and a uniform rectangular plate $R$ (sides $b$, $a$) have identical areas and masses. Show that $\frac{I_{\mathrm{xR}}}{I_{\mathrm{xS}}}<1$.

Show that
(a) $I_{xR}+I_{xS}<1$
(b) $I_{yR}/I_{yS}>1$
(c) $I_{zR}/I_{zS}>1$

A symmetric lamina of mass $M$ consists of a square shape with a semicircular section over each of the edge of the square, as in the figure. The side of the square is $2a$. The moment of inertia of the lamina about an axis through its centre of mass and perpendicular to the plane is $1.6M{a}^2$ Find the moment of inertia of the lamina about the tangent $\mathrm{AB}$ in the plane of lamina.

A uniform square plate has a small piece $Q$ of an irregular shape removed and glued to the centre of the plate leaving a hole behind, as shown in the figure. The moment of inertia about $z$-axis is then

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

Moment of inertia of a uniform triangular plate about axis passing through sides $AB\mathit{,}AC$ and $BC$ are $I_{\mathrm{p}},I_{\mathrm{B}}$and $I_{\mathrm{H}}$, respectively and about an axis perpendicular to the plane and passing through point $\mathrm{C}$ is $I_{\mathrm{C}}.$ Then:

A ring of mass $M$ and radius $R$ lies in the $x-y$ plane with its centre at the origin, as shown. The mass distribution of ring is non-uniform such that, at any point $\mathrm{P}$ on the ring, the mass per unit length is given by $\lambda ={\lambda }_0{\cos }^2\left(\theta \right)$ (where ${\text{λ}}_0$ is a positive constant). Then, the moment of inertia of the ring about $z$ axis is: