Explain the motion of blocks connected by a string in (i) vertical motion (ii) horizontal motion .

Explanation

Vertical motion : Let us consider two blocks of masses `m_(1)` and `m_(2) (m_(1) gt m_(2))` connected by a light and inextensible string that passes over a pulley

Let the tension in the string be T and acceleration a When the system is released both the blocks both the start moving `m_(2)` vertically upward with same acceleration a. The gravitational force `m_(1)`g on mass `m_(1)` is used to lift the mass `m_(2)`
the upward direction is selected as y direction . the free body diagrams of both masses.

Horizontal motion : in this case mass `m_(2)` is kept on a horizontal table and mass `m_(1)` is hanging through a smalll pulley it is assumed that there is no friction on the surface

As both the blocks are connected to the unstrechable string if `m_(1)` moves with an acclereation a downward athen `m_(2)` also moves iwth the same acceleration a horizontally
The forces acting on mass `m_(2)` are
(i) horizontal tension (T) exerted by the string
(ii) upward normal force (N) exerted by the surface
(iii) Downard normal gravitational force `(m_(2)g)`
The forces acting on mass `m_(1)` are
(i)Tension (T) acting upwards
(ii) Downward gravitational force `(m_(1)g)` the free body diagrams for both the masses is