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Question

A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is mass less and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity stack v with rightwards arrow on top subscript 0 end subscript equals stack V with rightwards arrow on top subscript 0 end subscript stack i with tilde on top. The coefficient of friction is mu The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is

  1. – kx    
  2. – 2kx    
  3. negative fraction numerator 2 k x over denominator 3 end fraction    
  4. negative fraction numerator 4 k x over denominator 3 end fraction    

The correct answer is: negative fraction numerator 4 k x over denominator 3 end fraction

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