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Question

A disc of mass 2 M and radius R is placed on a fixed plank (rough) of length L. The coefficient of friction between the plank and disc is mu = 0.5. String (light) is connected to centre of disc and passing over a smooth light pulley and connected to a block of mass M as shown in the figure. Now the disc is given an angular velocity omega subscript 0 end subscript in clockwise direction and is gently placed on the plank. Consider this instant as t=0. Based on above information, answer the following questions: Time t subscript 0 end subscript1 at which the disc will cross the other end of the plank is-

  1. square root of fraction numerator 8 L over denominator g end fraction end root    
  2. fraction numerator omega subscript 0 end subscript R over denominator g end fraction plus square root of fraction numerator 8 L over denominator g end fraction end root    
  3. square root of fraction numerator 8 L over denominator g end fraction end root plus fraction numerator 4 omega subscript 0 end subscript R over denominator g end fraction    
  4. square root of fraction numerator omega subscript 0 end subscript R over denominator g end fraction end root plus square root of fraction numerator 4 L over denominator g end fraction end root    

The correct answer is: fraction numerator omega subscript 0 end subscript R over denominator g end fraction plus square root of fraction numerator 8 L over denominator g end fraction end root


    Mg – T = Ma ...(i)T – f r = 2Ma ...(ii)

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