we know that in rolling motion the top of drum has linear velocity 2v if the centre of mass has linear velocity v. thus if a board moves over a drum without slipping it wil roll 2vt=2L if the center of mass moves vt=L in time t, and this result is independent of size of the drum. but when i do this with a pen or pencil rolling by my hand i always find that the pen moves the distance equal to length of my hand. do it yourself and please comment on this.
So you are claiming that when you roll your hand over a pen, that the pen moves at the same rate as your hand? So if you start with the pen at your fingertips, the pen remains at your fingertips as your hand moves? I don't see how that is possible. Better try that again!
i am saying that when i roll the pen under my hand from fingertips to end of palm without letting my hand slip over the pen, the pen traverse the same distance as the length of my palm which it should cover only half of the length.
Compare the distance your hand moves with respect to the table with the distance the pen moves. Your hand moves twice as far. Thus your hand moves with respect to the pen (which is moving) the same distance that the pen moves with respect to the table. This is what you are describing, which makes perfect sense.