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'.