# Inner and other radii of a spool are and respectively. A thread is wound over its inner surface and spool is placed over a rough horizontal surface. Thread is pulled by a force  as shown in Fig.In case of pure rolling, which of the following statements are false? a) Thread unwinds, spool rotates anticlockwise and friction acts leftwards b) Thread winds, spool rotates clockwise and friction acts leftwards c) Thread winds, spool moves to the right and friction acts rightwards d) Thread winds, spool moves to the right and friction does not come into existence

## Question ID - 100610 :- Inner and other radii of a spool are and respectively. A thread is wound over its inner surface and spool is placed over a rough horizontal surface. Thread is pulled by a force  as shown in Fig.In case of pure rolling, which of the following statements are false? a) Thread unwinds, spool rotates anticlockwise and friction acts leftwards b) Thread winds, spool rotates clockwise and friction acts leftwards c) Thread winds, spool moves to the right and friction acts rightwards d) Thread winds, spool moves to the right and friction does not come into existence

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(a,c,d)

Since, the spool rolls over the horizontal surface, instantaneous axis of rotation passes through the point of contact of spool with the horizontal surface

About the instantaneous axis of rotation, moment produced by  is clockwise. Therefore, the spool rotates clockwise. In that case, acceleration will be rightward and thread will wind

If rotation motion of the spool is considered about its own, then the resultant moment on it must be clockwise. But moment produced by the force is anticlockwise and its magnitude is equal to . Hence, moment produced by the friction (about its own axis) must be clockwise and its magnitude must be greater than  It is possible only when friction acts leftwards. Therefore, option (b) is correct

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A flat cart of mass  starts moving to the right due to a constant horizontal force  at . Sand spills on the flat cart from a stationary hopper. The velocity of loading is constant and is equal  kg/s

 a) Initial acceleration is equal to b) Acceleration at time  is c) Kinetic energy of loaded cart at an instant is equal to work done by force  up to that instant d) Momentum of loaded cart at an instant is equal to impulse of force  up to that instant