Physics-
General
Easy

Question

The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant k and compresses it by length L. The maximum momentum of the block after collides is

  1. square root of M k L end root    
  2. fraction numerator k L to the power of 2 end exponent over denominator 2 M end fraction    
  3. Zero    
  4. fraction numerator M L to the power of 2 end exponent over denominator k end fraction    

The correct answer is: square root of M k L end root


    Momentum would be maximum when KE would be maximum and this is the case when total elastic PE is converted KE.
    According to conservation of energy
    fraction numerator 1 over denominator 2 end fraction k L to the power of 2 end exponent equals fraction numerator 1 over denominator 2 end fraction M v to the power of 2 end exponent
    Or k L to the power of 2 end exponent equals fraction numerator open parentheses M v close parentheses to the power of 2 end exponent over denominator M end fraction
    M K L to the power of 2 end exponent equals p to the power of 2 end exponent left parenthesis p equals M v right parenthesis
    therefore p equals L square root of M K end root

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