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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°C–1. The reading of scale at 40°C is-

  1. 10.01 cm    
  2. 10.004 cm    
  3. 10.006cm    
  4. 10.04 cm    

The correct answer is: 10.004 cm


    because T V equals S R open parentheses 1 plus alpha subscript g end subscript capital delta T close parentheses equals open parentheses T V close parentheses open parentheses 1 minus alpha subscript g end subscript capital delta T close parentheses
    therefore S R equals left parenthesis T V right parenthesis left parenthesis 1 plus alpha g capital delta T right parenthesis to the power of negative 1 end exponent equals left parenthesis 10.006 right parenthesis open parentheses 1 minus 10 to the power of negative 5 end exponent cross times 20 close parentheses equals 10.006 minus 0.002 equals 10.004 c

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