The distance between the vertex and the centre of mass of a uniform solid planar circular segment of angular size $\theta$ and radius $R$ is given by

$A$ uniform circular disc of radius $a$ is taken. $A$ circular portion of radius $b$ has been removed from it as shown in the figure. If the centre of the hole is at a distance $c$ from the centre of the disc,the distance $x_2$ of the centre of mass of the remaining part from the initial centre of mass $O$ is given by

$A$ uniform square plate is shown in the figure. Four identical small squares are removed from its corners. If squares $1, 2,$ and $3$ are removed,where will the center of mass $(C.M.)$ be located?

The sector of a circular plate shown in the figure has its center of mass at $y_{CM} =$

$A$ circular hole of radius $R/2$ is cut from a circular disc of mass $M$ and radius $R$ such that the circumference of the hole passes through the center of the disc. What is the moment of inertia of the remaining part about an axis perpendicular to the plane of the disc and passing through its center?

$A$ ring is formed by joining two uniform semi-circular rings $ABC$ and $ADC$. The mass of $ABC$ is thrice that of $ADC$. If the ring is hinged to a fixed support at $A$,it can rotate freely in a vertical plane. Find the value of $\tan \theta$,where $\theta$ is the angle made by the line $AC$ with the vertical in equilibrium.