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At 20 to the power of ring operator end exponent C a liquid is filled upto 10 cm height in a container of glass of length 20 cm and cross-sectional area 100 cm2 Scale is marked on the surface of container. This scale gives correct reading at 20 to the power of ring operator end exponent C.text  Given  end text gamma subscript L end subscript equals 5 cross times 10 to the power of negative 5 end exponent k to the power of negative 1 end exponent comma alpha subscript g end subscript equals 1 cross times 10 to the power of negative 5 end exponent°C1.The actual height of liquid at 40°C is-

  1. 10.01 cm    
  2. 10.006 cm    
  3. 10.6 cm    
  4. 10.1 c    

The correct answer is: 10.006 cm


    A equals A subscript 0 end subscript open parentheses 1 plus 2 alpha subscript b end subscript capital delta T close parentheses equals 100 open parentheses 1 plus 2 cross times 10 to the power of negative 5 end exponent cross times 20 close parentheses equals 100.04 c m to the power of 2 end exponent
    Actual height of liquidfraction numerator text  Actual volume of liquid  end text over denominator text  cross – sectional area of vessel  end text end fraction equals fraction numerator 1001 over denominator 100.04 end fraction equals left parenthesis 1001 right parenthesis left parenthesis 100 plus 0.04 right parenthesis to the power of negative 1 end exponent blank
    equals open parentheses fraction numerator 1001 over denominator 100 end fraction close parentheses open parentheses 1 plus fraction numerator 0.04 over denominator 100 end fraction close parentheses to the power of negative 1 end exponent equals fraction numerator open parentheses 1001 close parentheses over denominator 100 end fraction open parentheses 1 minus fraction numerator 0.04 over denominator 100 end fraction close parentheses equals fraction numerator 1 over denominator 100 end fraction open parentheses 1001 minus 0.4 close parentheses equals 10.006 c m

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