A spool of inner radius 'r' and outer radius 'R' is wound by a thread and the free end of the thread is passed over a nail and is pulled with velocity 'v'. (The spool is on the ground).What is the velocity of the spool when the thread makes an angle  with the vertical ?

V x (R/r + sin )

I pondered over this Question and found that my previous ans was  wrong

I m sure the ans is V / ( R\r  - sin).

Let V* be velocity of spool

The working method is that   R= V* in rolling  where  is ang.vel

also at point of pulling V = r  -  V*sin.

Solve these eq to get ans

The question isn't complete ... From which cylinder does the thred finally come out?? Top or bottom?

I am assuming the the string comes out of the bottom of the inner cylinder at the bottom

The horizontal component of the velocity is

Let the velocity of the spool's center be and its angular velocity about the centre be

For no slipping

Also