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In an experiment to determine Young's modulus of a wire, the formula used is Y = 4MgL d^2 l . The percentage errors in the measurement of mass M , original length L , diameter d , and extension l are 1 % , 1.5 % , 3 % , and 2.5 % respectively. The maximum percentage error in the calculated value of Young's modulus Y is

Options

  1. A6 %
  2. B11 %
  3. C8 %
  4. D14 %

Correct answer

B. 11 %

Step-by-step solution

The formula for Young's modulus is given by Y = 4MgL d^2 l . Here, 4 , g , and are constants and do not contribute to the percentage error. The maximum percentage error in Y is given by the sum of the individual relative errors multiplied by their respective powers: ( Y Y ) 100 = ( M M ) 100 + ( L L ) 100 + 2 ( d d ) 100 + ( l l ) 100 Substituting the given percentage errors: ( Y Y ) 100 = 1 % + 1.5 % + 2(3 %) + 2.5 % ( Y Y ) 100 = 1 % + 1.5 % + 6 % + 2.5 % = 11 % . Answer: 11 %

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