Three identical particles are placed on a horizontal smooth table, connected with strings as shown. The particle $B$ is imparted a velocity $v_0=9 \mathrm{m}/\mathrm{s}$ in horizontal direction perpendicular to the line $ABC.$ The speed (in $\mathrm{m}/\mathrm{s}$ ) of particle $A$ when it is about to collide with $C.$

A uniform square plate from which four identical squares at the corners will be removed is shown in figure.
Answer the following questions on the basis of above data.

(i) Where is the centre of mass of the uncut plate?
(ii) Where does $\mathrm{CM}$ (centre of mass) lie after square $1$ is removed?
(iii) Where does $\mathrm{CM}$ lie after squares $1$ and $2$ are removed?
(iv) Where does $\mathrm{CM}$ lie after squares $1$ and $3$ are removed?

(v) Where does $\mathrm{CM}$ lie after squares $1\text{,} 2$ and $3$ are removed?
(vi) Where does $\mathrm{CM}$ lie after all the four squares are removed?
(Give Answers in terms of quadrants and axes.)

Find the $\mathrm{CM}$ of the system of a L-shaped rod of mass $m$ and a particle of mass $m$ attached at the end of the rod as shown.

A ring and a particle of masses $2 m$ and $m$ are kept as shown in the figure, such that the $\mathrm{CM}$ of the combination lies at the origin. Find $x.$

Find $x$ and $y$ coordinates of the centre of mass of the plate shown in figure from which a square of side $2 \mathrm{m}$ is cut out.

Find centre of mass distance from point $O$ of the uniform circular arc shown in figure.

Determine th coordinate of centre of mass of a thin homogeneous plate having the form of a rectangle with sides $r$ and $2 r$ from which a semicircle with a radius $r$ is cut out.

The figure shows a square metal plate of side $l$ from which a square plate of side $a$ has been cut as shown in the figure. Find the ratio $\left(a/l\right)$ so that the centre of mass of the remaining L-shaped plate coincides with the point $A.$

Figure shows a fixed wedge on which two blocks of masses $2 \mathrm{kg}$ and $3 \mathrm{kg}$ are placed on its smooth inclined surfaces. When the two blocks are released from rest, find the acceleration of centre of mass of the two blocks.