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Question

A plank having mass M is placed on smooth horizontal surface. Block of mass m is placed on it coefficient of friction between block and plank is mu subscript 0 end subscript plus k x, where k is constant and x is relative displacement between block and plank. A force F is applied on block where F = at, where a = 10; t is in second. Find t0 when relative motion will occur between block and plank

  1. mu subscript 0 end subscript M plus fraction numerator mu subscript 0 end subscript M to the power of 2 end exponent over denominator m end fraction    
  2. mu subscript 0 end subscript m plus fraction numerator mu subscript 0 end subscript M to the power of 2 end exponent over denominator m end fraction    
  3. mu subscript 0 end subscript m plus fraction numerator mu subscript 0 end subscript m to the power of 2 end exponent over denominator M end fraction    
  4. mu subscript 0 end subscript M plus fraction numerator mu subscript 0 end subscript m to the power of 2 end exponent over denominator M end fraction    

The correct answer is: mu subscript 0 end subscript m plus fraction numerator mu subscript 0 end subscript m to the power of 2 end exponent over denominator M end fraction


    Let at time t0 relative motion will occur

    mu subscript 0 end subscript m g equals M a (1)

    10 t subscript 0 end subscript minus mu subscript 0 end subscript m g equals m a (2)
    From (1) and (2) ;
    t subscript 0 end subscript equals mu subscript 0 end subscript m plus fraction numerator mu subscript 0 end subscript m to the power of 2 end exponent over denominator M end fraction

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