A $2kg$ body and a $3kg$ body are moving along the x-axis. At a particular instant, the $2kg$ body is $1m$ from the origin and has a velocity of $3ms^{-1}$ and the $3kg$ body is $2m$ from the origin and has velocity of $-1 ms^{-1}$. Find the position and velocity of the centre of mass and also find the total momentum.
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The x-coordinate of the COM is given by, $\text{x}=\frac{\text{m}_1\text{x}_1+\text{m}_2\text{x}_2}{\text{m}_1+\text{m}_2}$ $=\frac{2\times1+3\times2}{2+3}=\frac{8}{5}=1.6\text{m}$ Velocity of the COM is given by, $\text{V}=\frac{\text{m}_1\text{v}_1+\text{m}_2\text{v}_2}{\text{m}_1+\text{v}_1}$ $=\frac{2\times3+3\times(-1)}{2+3}=\frac{3}{5}=0.6\text{ms}^{-1}$ Total momentum $=(\text{m}_1+\text{m}_2)\text{V}$ $=(2+3)\times0.6=3\text{kg ms}^{-1}$
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