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.

There are two masses $m_1$ and $m_2$ placed at a distance $l$ apart, let the centre of mass of this system is at a point named $C.$ If $m_1$ is displaced by $l_1$ towards $C$ and $m_2$ is displaced by $l_2$ away from $C,$ find the distance from $C$where the new centre of mass will be located.

Let there are three equal masses situated at the vertices of an equilateral triangle, as shown in figure. Now particle $A$ starts with a velocity $v_1$ towards line $A B,$ particle $B$ starts with the velocity $v_2$ towards line$B C$ and particle $C$ starts with velocity $v_3$ towards line$C A.$ Find the displacement of the centre of mass of the three particles $A, B$ and $C$ after time $t .$ What would it be if $v_1=v_2=v_3$ ?

Figure shows a flat car of mass $M$ on a frictionless road. $A$ small massless wedge is fitted on it as shown. $A$ small ball of mass $m$ is released from the top of the wedge, it slides over it and falls in the hole at distance $l$ from the initial position of the ball. Find the distance the flat car moves till the ball gets into the hole.

A cart of mass $M$ is at rest on a frictionless horizontal surface and a pendulum bob of mass $m$ hangs from the roof of the cart. The string breaks, the bob falls on the floor, makes several collisions on the floor and finally lands up in a small slot made in the floor. The horizontal distance between the string and the slot is $L.$ Find the displacement of the cart during this process.

Find the displacement of the wedge when $\mathrm{m}$ comes out of the wedge. There is no friction anywhere.

A block of mass $m$ is initially lying on a wedge of mass $M$ with an angle of inclination $\theta$, as shown in figure. Calculate the displacement of the wedge when the block is released and reaches to the bottom of the wedge.