A circular stage is free to rotate about vertical axis passing through centre. $A$ tortoise is  sitting at corner of stage. Stage is provided angular velocity $\omega_0$. If tortoise start  moving along one chord at constant speed with respect to stage then how the angular  velocity of stage $\omega(t)$ vary with time $t$ :-

The given figure shows a disc of mass $M$ and radius $R$ lying in the $x-y$ plane with its centre on $x$ axis at a distance a from the origin. then the moment of inertia of the disc about the $x-$ axis is

A circular disc of radius $R$ has a uniform thickness. A circular hole of diameter equal  to the radius of disc has been cut out as shown. Distance of centre of mass of the  remaining disc from point $O$ is

Four masses are fixed on a massless rod as shown in Fig. The moment of inertia about the axis $P$ is about ....... $kg-m^2$

A uniform rod of mass $m$ and length $l$ rotates in a horizontal plane with an angular velocity $\omega $ about a vertical axis passing through one end. The tension in the rod at a distance $x$ from the axis is

From a solid sphere of mass $M$ and radius $R$ a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is