Physics-
General
Easy

Question

A piece of copper wire has twice the radius of a piece of steel wire. Young’s modulus for steel is twice that of the copper. One end of the copper wire is joined to one end of the steel wire so that both can be subjected to the same longitudinal force. By what fraction of its length will the steel have stretched when the length of the copper has increased by 1%?

  1. 1 percent sign    
  2. 2 percent sign    
  3. 2.5percent sign    
  4. 3 percent sign    

The correct answer is: 2 percent sign


    increment l equals fraction numerator F l over denominator pi r to the power of 2 end exponent Y end fraction o r fraction numerator increment l over denominator l end fraction proportional to fraction numerator 1 over denominator r to the power of 2 end exponent Y end fraction
    fraction numerator open parentheses fraction numerator increment l over denominator l end fraction close parentheses subscript s end subscript over denominator open parentheses fraction numerator increment l over denominator l end fraction close parentheses subscript C u end subscript end fraction equals fraction numerator r subscript C u end subscript superscript 2 end superscript blank C u over denominator r subscript s end subscript superscript 2 end superscript Y subscript 3 end subscript end fraction equals fraction numerator 4 r subscript s end subscript superscript 2 end superscript fraction numerator Y subscript s end subscript over denominator blank 2 end fraction over denominator r subscript s blank end subscript superscript 2 end superscript Y subscript s end subscript end fraction equals 2
    therefore blank open parentheses fraction numerator increment l over denominator l end fraction close parentheses subscript s end subscript equals 2 open parentheses fraction numerator increment l over denominator l end fraction close parentheses subscript C u end subscript

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