# A cylinder rolls without slipping on a rough horizontal floor, its centre of mass moving with speed v. It makes an elastic collision with a smooth vertical wall. After impact

1) its centre of mass will move with a speed V.

2) its motion will be rolling without slipping.

3) the motion will be rolling with slipping initially and its rotational motion will stop momentarily at some instant .

4) its motion will be rolling with out slipping only after some times.

Which one is the correct answer ?

a) 1,2 and 4 b) 1,2 and 3 c) 1,3 and 4 d) 2,3 and 4

Since the force of impact is normal to the surface of cylinder, and its an elastic impact, velocity of centre of mass changes direction.
$w$ however does not change and there will be slipping.
However, Since friction will now act backward, it will start rolling after some time.
$w$ will become zero.
edited Jun 24, 2014