A circular plate of uniform thickness has a diameter of $28 \mathrm{cm}.$ A circular portion of diameter $21 \mathrm{cm}$ is removed from the plate as shown. $O$ is the centre of mass of complete plate. The position of centre of mass of remaining portion will shift towards left from ' $O$ ' by

Figure shows a thin uniform $rod50 \mathrm{cm}$ long and has a mass of $100 \mathrm{g}.$ A hollow metal ball is filled with air and has a diameter $10 \mathrm{cm}$ and total mass $50 \mathrm{g}$ is fixed to one end of the rod. At what point along its length will the ball and rod balance horizontally?

Three particles of equal masses are placed at the corners of an equilateral triangle as shown in the figure. Now particle $A$ starts with a velocity $v_1$ towards line $A B,$ particle $B$ starts with a velocity $v_2$ towards line $B C$ and particle $C$ starts with velocity $v_3$ towards line $C A.$The displacement of $\mathrm{CM}$ of three particle $A, B$ and $C$ after time $t$ will be $($given if $\left.v_1=v_2=v_3\right)$ 

Three point like equal masses $m_1, m_2$ and $m_3$ are connected to the cnds of a massless rod of length  $L$ which lies at rest on a smooth horizontal plane (see figure). At $t=0,$ an explosion occurs between $m_2$ and $m_3,$ and as a result, mass $m_3$ is detached from the rod, and moves with a known velocity $y$ at an angle of $30°$ with the $y$ -axis. Assume that the masses $m_2$ and $m_3$ are unchanged during the explosion. What is the velocity of the centre of mass of the system consisting of three masses, after the explosion?

Three particles of masses $1 \mathrm{kg}, 2 \mathrm{kg}$ and $3 \mathrm{kg}$ are situated at the corners of an equilateral triangle move at speed $6{ \mathrm{ms}}^{-1},$ $3{ \mathrm{ms}}^{-1}$  and $2{ \mathrm{ms}}^{-1}$ respectively. Each particle maintains a direction towards the particle at the next corner symmetrically. Find velocity of $\mathrm{CM}$ of the system at this instant.