Physics-
General
Easy

Question

An open knife edge of mass 'm' is dropped from a height 'h' on a wooden floor. If the blade penetrates upto the depth 'd' into the wood, the average resistance offered by the wood to the knife edge is

  1. m g    
  2. m g open parentheses 1 minus fraction numerator h over denominator d end fraction close parentheses    
  3. m g open parentheses 1 plus fraction numerator h over denominator d end fraction close parentheses    
  4. m g open parentheses 1 plus fraction numerator h over denominator d end fraction close parentheses to the power of 2 end exponent    

The correct answer is: m g open parentheses 1 plus fraction numerator h over denominator d end fraction close parentheses


    Let the blade stops at depth d into the wood.

    v to the power of 2 end exponent equals u to the power of 2 end exponent plus 2 a S
    Þ 0 equals left parenthesis square root of 2 g h end root right parenthesis to the power of 2 end exponent plus 2 left parenthesis g minus a right parenthesis d
    by solving a equals open parentheses 1 plus fraction numerator h over denominator d end fraction close parentheses g
    So the resistance offered by the wood equals m g open parentheses 1 plus fraction numerator h over denominator d end fraction close parentheses

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