Motion of two bodies - Smooth surface and smooth pulley:

THE HORIZONTAL SURFACE IS SMOOTH AND STRING IS PASSING OVER SMOOTH PULLEY:

Figure shows two weights W₁ and W₂ connected by light inextensible string, passing over smooth pulley. The weight W₂ is placed on smooth horizontal surface, while the weight W₁ is hanging free. The weight W1 is moving in down direction, while weight W₂ is moving on smooth horizontal surface. The velocity and acceleration of W₁  is same as that of W₂ . As string is light and inextensible and is passing over smooth pulley, the tensions of string will be same on both the sides of pulley.

For W₁ block: Move down

W₁  - T = (W₁/g).a                                                                                                                              ...(1)

For W₂ block

T = (W₂/g).a                                                                                                                              ...(2)

(As W act vertically and T act horizontally and w.cos90 = 0)

Solve both equations for value of 'T' and 'a'.