A uniform wire of length $l$ is bent into the shape of '$V$' as shown. The distance of its centre of mass from the vertex $A$ is:-

Three man $A,B$ and $C$ of mass $40 \mathrm{kg}, 50 \mathrm{kg}$ and $60 \mathrm{kg}$ are standing on a plank of mass $90 \mathrm{kg}$, which is kept on a smooth horizontal plane. If $A$ and $C$ exchange their positions then mass $B$ will shift:-

Infinite numbers of blocks are placed on a table edge as shown in the digram.

What is the minimum value of $L$ so that the blocks are just going to topple over the table?

Considering a system having two masses $m_1$ and $m_2$ in which first mass is pushed towards centre of mass by a distance a, the distance required to be moved for second mass to keep centre of mass at same position is:-

As shown, big box of mass $M$ is resting on a horizontal smooth floor. On the bottom of the box there is a small block of mass $m$. The block is given an initial speed $v_0$ relative to the floor, and starts to bounce back and forth between the two walls of the box. Find the final speed of the box when the block has finally come to rest in the box:-

Two balls of masses $m_1,m_2$ and speeds $v_1$ and $v_2$ collide at right angle. The maximum amount of kinetic energy loss due to inelastic collision is _____.

The velocity of centre of mass of the system as shown in the figure:-