Three bodies having masses $5 \, kg$,$4 \, kg$,and $2 \, kg$ are moving at speeds of $5 \, m/s$,$4 \, m/s$,and $2 \, m/s$ respectively along the $X$-axis. The magnitude of the velocity of the centre of mass is (in $m/s$):

Two particles of masses $m_1$ and $m_2$ initially at rest start moving towards each other under their mutual force of attraction. The speed of the centre of mass at any time $t$,when they are at a distance $r$ apart,is

Two identical bodies $A$ and $B$ of equal masses have initial velocities $v_1 = 4\hat{i} \text{ m/s}$ and $v_2 = 4\hat{j} \text{ m/s}$ respectively. The body $A$ has acceleration $a_1 = 6\hat{i} + 6\hat{j} \text{ m/s}^2$ while the acceleration of the other body $B$ is zero. The centre of mass of the two bodies moves in . . . . . . path.

Obtain Newton's second law for a system of particles and write its statement.

Two particles of mass $m$ each are fixed at the opposite ends of a massless rod of length $5 \ m$ which is oriented vertically on a smooth horizontal surface and released. Find the displacement of the lower mass on the ground when the rod makes an angle of $37^o$ with the vertical. (in $m$)

The equation $M\vec{A} = \vec{F}_{ext}$ denotes what?