IIT (NTSE/Olympiad)  

Newton's Laws Of Motion & Friction

8. Motion of bodies in contact

8. Motion of connected Bodies
Case (A) :
For two Bodies :
F is the pull on body A of mass m1. The pull of A on B is exercised as tension through the string connecting A and B. The value of tension throughout the string is T only.
But this manifests as a pull T on B and a "reaction pull" T on A the free body diagram in this case are shown as follows.

Note : The spring is massless
Free body diagrams :
For body AFor body B
R1= m1g
F – T = m1a
R2= m2g
T = m2a

Case (B) :
For Three bodies :

Free body diagrams :
For AFor BFor C

R1= m1g
T1= m1a

R2= m2g
T2– T1= m2a
⇒ T2= m2a + T1
T2= (m2 + m1)a

R3= m3g
F – T2= m3a
⇒ F = m3a + T2
= m3a + (m1 + m2)a
F = (m1 + m2 + m3)a

IIT (Class X)