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Question

A ball of radius r and density r falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is h, the value of h is given by

  1. fraction numerator 2 over denominator 9 end fraction r to the power of 2 end exponent open parentheses fraction numerator 1 minus rho over denominator eta end fraction close parentheses g    
  2. fraction numerator 2 over denominator 81 end fraction r to the power of 2 end exponent open parentheses fraction numerator rho minus 1 over denominator eta end fraction close parentheses g    
  3. fraction numerator 2 over denominator 81 end fraction r to the power of 4 end exponent open parentheses fraction numerator rho minus 1 over denominator eta end fraction close parentheses to the power of 2 end exponent g    
  4. fraction numerator 2 over denominator 9 end fraction r to the power of 4 end exponent open parentheses fraction numerator rho minus 1 over denominator eta end fraction close parentheses to the power of 2 end exponent g    

The correct answer is: fraction numerator 2 over denominator 81 end fraction r to the power of 4 end exponent open parentheses fraction numerator rho minus 1 over denominator eta end fraction close parentheses to the power of 2 end exponent g


    Velocity of ball when it strikes the water surface v equals square root of 2 g h end root …(i)
    Terminal velocity of ball inside the water v equals fraction numerator 2 over denominator 9 end fraction r to the power of 2 end exponent g fraction numerator open parentheses rho minus 1 close parentheses over denominator eta end fraction …(ii)
    Equating (i) and (ii) we get square root of 2 g h end root equals fraction numerator 2 over denominator 9 end fraction fraction numerator r to the power of 2 end exponent g over denominator eta end fraction left parenthesis rho minus 1 right parenthesis
    Þ h equals fraction numerator 2 over denominator 81 end fraction r to the power of 4 end exponent open parentheses fraction numerator rho minus 1 over denominator eta end fraction close parentheses to the power of 2 end exponent g

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