Physics-
General
Easy

Question

Three rods of equal length l are joined to form an equilateral triangle P Q R. O is the mid point of P Q. Distance O R remains same for small change in temperature. Coefficient of linear expansion for P R and R Q is same, i. e. comma blank alpha subscript 2 end subscript but that for P Q is alpha subscript 1 end subscript. Then

  1. alpha subscript 2 end subscript equals 3 alpha subscript 1 end subscript    
  2. alpha subscript 2 end subscript equals 4 alpha subscript 1 end subscript    
  3. alpha subscript 1 end subscript equals 3 alpha subscript 2 end subscript    
  4. alpha subscript 1 end subscript equals 4 alpha subscript 2 end subscript    

The correct answer is: alpha subscript 1 end subscript equals 4 alpha subscript 2 end subscript


    open parentheses O R close parentheses to the power of 2 end exponent equals open parentheses P R close parentheses to the power of 2 end exponent minus open parentheses P O close parentheses to the power of 2 end exponent equals l to the power of 2 end exponent minus open parentheses fraction numerator l over denominator 2 end fraction close parentheses to the power of 2 end exponent
    equals open square brackets l open parentheses 1 plus alpha subscript 2 end subscript t close parentheses close square brackets to the power of 2 end exponent minus open square brackets fraction numerator l over denominator 2 end fraction open parentheses 1 plus alpha subscript 1 end subscript t close parentheses close square brackets to the power of 2 end exponentl to the power of 2 end exponent minus fraction numerator l to the power of 2 end exponent over denominator 4 end fraction equals l to the power of 2 end exponent open parentheses 1 plus alpha subscript 2 end subscript superscript 2 end superscript t to the power of 2 end exponent plus 2 alpha subscript 2 end subscript t close parentheses minus fraction numerator l to the power of 2 end exponent over denominator 4 end fraction left parenthesis 1 plus alpha subscript 1 end subscript superscript 2 end superscript t to the power of 2 end exponent plus 2 alpha subscript 1 end subscript t right parenthesis
    Neglecting alpha subscript 2 end subscript superscript 2 end superscript t to the power of 2 end exponent and alpha subscript 1 end subscript superscript 2 end superscript t to the power of 2 end exponent
    0 equals l to the power of 2 end exponent open parentheses 2 alpha subscript 2 end subscript t close parentheses minus fraction numerator l to the power of 2 end exponent over denominator 4 end fraction open parentheses 2 alpha subscript 1 end subscript t close parentheses rightwards double arrow 2 alpha subscript 2 end subscript equals fraction numerator 2 alpha subscript 1 end subscript over denominator 4 end fraction rightwards double arrow alpha subscript 1 end subscript equals 4 alpha subscript 2 end subscript

    Related Questions to study

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.