Physics-
General
Easy

Question

Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows

  1. L = 100 cm, r = 1mm    
  2. L = 200 cm, r = 3mm    
  3. L = 300 cm, r = 3mm    
  4. L = 400 cm, r = 4mm    

The correct answer is: L = 100 cm, r = 1mm


    increment L equals fraction numerator F L over denominator A Y end fraction
    Because, wires of the same material are stretched by the same load. So, F and Y will be constant.
    therefore blank increment L proportional to fraction numerator L over denominator pi r to the power of 2 end exponent end fraction
    increment L subscript 1 end subscript equals fraction numerator 100 over denominator pi cross times left parenthesis 1 cross times 10 to the power of negative 3 end exponent right parenthesis to the power of 2 end exponent end fraction equals fraction numerator 100 over denominator pi cross times 10 to the power of negative 6 end exponent end fraction
    equals fraction numerator 100 over denominator pi end fraction cross times 10 to the power of negative 6 end exponent
    therefore increment L subscript 2 end subscript equals fraction numerator 200 over denominator pi cross times left parenthesis 3 cross times 10 to the power of negative 3 end exponent right parenthesis to the power of 2 end exponent end fraction equals fraction numerator 200 over denominator pi cross times 9 cross times 10 to the power of negative 6 end exponent end fraction
    equals fraction numerator 22.2 over denominator pi end fraction cross times 10 to the power of 6 end exponent
    therefore increment L subscript 3 end subscript equals fraction numerator 300 over denominator pi cross times left parenthesis 3 cross times 10 to the power of negative 3 end exponent right parenthesis to the power of 2 end exponent end fraction equals fraction numerator 100 over denominator pi cross times 9 cross times 10 to the power of negative 6 end exponent end fraction
    equals fraction numerator 33.3 over denominator pi end fraction cross times 10 to the power of 6 end exponent
    therefore increment L subscript 4 end subscript equals fraction numerator 400 over denominator pi cross times left parenthesis 4 cross times 10 to the power of negative 3 end exponent right parenthesis to the power of 2 end exponent end fraction equals fraction numerator 400 over denominator pi cross times 16 cross times 10 to the power of negative 6 end exponent end fraction
    equals fraction numerator 25 over denominator pi end fraction cross times 10 to the power of 6 end exponent
    We can see that, L=100 cm and r = 1mm will elongate most.

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