Example $6$: An external force $F$ is applied to the stationary three particles as shown in the figure. If $m_1=1kg,m_2=2kg$ and $m_3=3kg$;

i$)$ Does the system move?

ii$)$ If yes, find the acceleration of the particles,

iii$)$ Find the forces on $m_2$ due to the $m_1$ and $m^2$