speed,length

A drum reel of inner dia 140 is used to roll paper is driven by a variable speed motor.the paper of 1mm thickness is fed at the speed of 100 meter/m
At what ratio the speed of reel driving motor will be brought down as the diameter of the reel is increasing after each rev.which formulas will be used to calculate

Math

I don't know any calculus, but if I were in the field, and needed this for some reason, here is how I would do it. It will not be "dead on" but close enough for a real world application (not for a test). Assuming that the initial diameter of 140 is in mm. After 1 revolution the new drum diameter will be 142mm, then 144mm etc. (don't forget your adding 1mm to each side)
The circumference of the drum will be pi multiplied by the diameter.
So for the first revolution, 140mm*pi yields 439.6mm (or .4396 M)for drum circumference. You are feeding at 100 meter/min. So the first revolution would take .4396/100 or .004396 minutes. Divide this into 1 and you get approx. 227 RPM.
From there I'd let Excel do the work with the copy/paste, so it could do calculations and derive any formula I would need.
A constant torque setup on your VFD would probably work a lot better.