Physics-
General
Easy

Question

Two wires, one made of copper and other of steel are joined end to end (as shown in figure). The area of cross-section of copper wire is twice that of steel wire.

They are placed under compressive force of magnitudes F. The ratio for their lengths such that change in lengths of both wires are same is (Y subscript s end subscript equals 2 cross times 10 to the power of 11 end exponent N m to the power of negative 2 end exponent blank a n d Y subscript c end subscript equals 1.1 cross times 10 to the power of 11 end exponent N m to the power of negative 2 end exponent right parenthesis

  1. 2.1    
  2. 1.1    
  3. 1.2    
  4. 2    

The correct answer is: 1.1


    Y subscript s end subscript equals fraction numerator F l subscript s end subscript over denominator A subscript s end subscript increment L subscript s end subscript end fraction
    And Y subscript C end subscript equals fraction numerator F L subscript C end subscript over denominator A subscript C end subscript increment L subscript C end subscript end fraction
    therefore fraction numerator L subscript C end subscript over denominator L subscript S end subscript end fraction blank equals blank fraction numerator fraction numerator Y subscript C end subscript A subscript C end subscript increment L subscript C end subscript over denominator F end fraction over denominator fraction numerator Y subscript S end subscript A subscript S end subscript increment L subscript S end subscript over denominator F end fraction end fraction equals open parentheses fraction numerator Y subscript C end subscript over denominator Y subscript S end subscript end fraction close parentheses open parentheses fraction numerator A subscript C end subscript over denominator A subscript S end subscript end fraction close parentheses open parentheses fraction numerator increment L subscript C end subscript over denominator increment L subscript S end subscript end fraction close parentheses
    Here, fraction numerator A subscript C end subscript over denominator A subscript S end subscript end fraction equals 2 comma fraction numerator increment L subscript C end subscript over denominator increment L subscript S end subscript end fraction equals 1 comma fraction numerator Y subscript C end subscript over denominator Y subscript S end subscript end fraction equals fraction numerator 1.1 over denominator 2 end fraction
    therefore fraction numerator L subscript C end subscript over denominator L subscript S end subscript end fraction equals fraction numerator 1.1 over denominator 2 end fraction blank cross times 2 blank cross times 1 equals 1.1

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