$\square \mathrm{ABCD}$  is a uniform square plate with four identical squares $1, 2, 3, 4$ placed at four corners. If squares $1$ and $2$ are removed, where will centre of mass lie? 

Three masses of $2 \mathrm{kg}, 12 \mathrm{kg}$ and $4 \mathrm{Kg}$ are connected to each other with threads and are placed on a table as shown in the figure. 

$g=10 \mathrm{m} {\mathrm{s}}^{-2},$ If the acceleration with which the system is moving is 

Let a force $\overrightarrow{\mathit{F}}$ act on a particle at point $P$ whose position with respect to origin $O$ is given by the position vector $r$ as shown in the figure. 

A man of mass $m_1$ holding one end of a massless, inextensible string that passes over the smooth pulley, is accelerating up while standing on a platform of mass $m_2$. If the pulley moves up with an upward acceleration $a$, the pressing force offered by the man on the platform is

At $t=0,$ force $F=kt$ is applied to a small body of mass $m$ resting on a smooth horizontal plane $(k$ is a constant $)$. The force is at an angle $\mathrm{\theta }$ with the horizontal.

Then the velocity of the body when its breaking off the plane is