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A rod of length 1000 mm and co-efficient of linear expansion alpha equals 10 to the power of negative 4 end exponent per degree is placed symmetrically between fixed walls separated by 1001 mm. The Young's modulus of the rod is 10 to the power of 11 end exponent N divided by m to the power of 2 end exponent. If the temperature is increased by 20 to the power of ring operator end exponent C, then the stress developed in therod is (in N divided by m to the power of 2 end exponent):

  1. 10    
  2. 10 to the power of 8 end exponent    
  3. 2 cross times 10 to the power of 8 end exponent    
  4. cannot be calculated    

The correct answer is: 10 to the power of 8 end exponent


    The change in length of rod due to increase in temperature in absence of walls iscapital delta l equals l alpha capital delta T equals 1000 cross times 10 to the power of negative 4 end exponent cross times 20 m m equals 2 m m
    But the rod can expand upto 1001 mm only. At that temperature its natural length is = 1002 mm.
    \ compression = 1mm
    \ mechanical stress =Y fraction numerator capital delta l over denominator l end fraction equals 10 to the power of 11 end exponent cross times fraction numerator 1 over denominator 1000 end fraction
    equals 10 to the power of 8 end exponent N divided by m to the power of 2 end exponent

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