A circular hole of radius $\left(\frac{ a }{2}\right)$ is cut out of a circular disc of radius $'a'$ as shown in figure. The centroid of the remaining circular portion with respect to point $'O'$ will be :

A uniform thin rod $AB$ of length $L$ has linear mass density $\mu \left( x \right) = a + \frac{{bx}}{L}$ , where $x$ is measured from $A$. If the $CM$ of the rod lies at a distance of $\left( {\frac{7}{12}} \right)L$ from $A$, then $a$ and $b$ are related as

In general form what are the coordinates of centre of mass of a rigid body.

Two objects of mass $10\,kg$ and $20\,kg$ respectively are connected to the two ends of a rigid rod of length $10\,m$ with negligible mass. The distance of the center of mass of the system from the $10\,kg$ mass is :

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 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

Sector of a circular plate shown in figure has position of centre of mass at $y_{CM} =$