Inner and outer radii of a spool are \( r \) and \( R \), respectively. A thread is wound over i...

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Inner and outer radii of a spool are \( r \) and \( R \), respectively. A thread is wound over its inner surface and spool is placed
\( \mathrm{P} \) over a rough horizontal surface. Thread is pulled by a force

W \( F \) as shown in figure. In case of pure rolling, which of the following statements are false?
(1) Thread unwinds, spool rotates anticlockwise and friction acts leftwards.
(2) Thread winds, spool rotates clockwise and friction acts leftwards.
(3) Thread winds, spool moves to the right and friction acts rightwards.
(4) Thread winds, spool moves to the right and friction does not come into existence.
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