Physics-
General
Easy

Question

The figure shows a glass tube (linear co-efficient of expansion is alpha) completely filled with a liquid of volume expansion co-efficient gamma. On heating length of the liquid column does not change. Choose the correct relation between gamma and alpha

  1. gamma equals alpha    
  2. gamma equals 2 alpha    
  3. gamma equals 3 alpha    
  4. gamma equals fraction numerator alpha over denominator 3 end fraction    

The correct answer is: gamma equals 2 alpha


    When length of the liquid column remains constant, then the level of liquid moves down with respect to the container, thus gamma must be less than 3 alpha
    Now we can write V equals V subscript 0 end subscript left parenthesis 1 plus gamma increment T right parenthesis
    Since V equals A l subscript 0 end subscript equals open square brackets A subscript 0 end subscript open parentheses 1 plus 2 alpha increment T close parentheses close square brackets l subscript 0 end subscript equals V subscript 0 end subscript open parentheses 1 plus 2 alpha increment T close parentheses
    Hence V subscript 0 end subscript open parentheses 1 plus gamma increment T close parentheses equals V subscript 0 end subscript open parentheses 1 plus 2 alpha increment T close parentheses rightwards double arrow gamma equals 2 alpha

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