A particle moves in a circle with constant angular velocity ω about a point P on its circumference. The angular velocity of particle about the centre C of the circle is

A solid sphere of radius $R$ has a moment of inertia $I$ about its geometrical axis. If it is melted into a disc of radius $r$ and thickness $t$. If it's moment of inertia about the tangential axis (which is perpendicular to the plane of the disc), is also equal to $I$, then the value of $r$ is equal to

A disc of mass $M$ and radius $R$ is lying on the $x\text{-}y$ plane. The locus of all points on the $x\text{-}y$ plane about which the moment of inertia of the rod is same as that about $0$ will be,

A thin rod of length $L$ and mass $M$ is bent at the middle point $O$ as shown in the figure. Consider an axis passing through two middle the point $O$ and perpendicular to the plane of the bent rod. Then the moment of inertia about this axis is