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A physical quantity W is defined by the relation W = A^2 B^3 C . The ratio of the percentage errors in the measurement of A , B , and C is 1 : 2 : 4 . If the total maximum percentage error in W is 30 % , the percentage error in the measurement of quantity B is

Options

  1. A3 %
  2. B10 %
  3. C6 %
  4. D5 %

Correct answer

C. 6 %

Step-by-step solution

The given relation is W = A^2 B^3 C . Let the percentage errors in the measurement of A , B , and C be x , 2x , and 4x respectively, as their ratio is 1 : 2 : 4 . The maximum percentage error in W is given by: ( W W ) 100 = 2 ( A A 100 ) + 3 ( B B 100 ) + 1 2 ( C C 100 ) Substituting the assumed percentage errors: ( W W ) 100 = 2(x) + 3(2x) + 1 2 (4x) ( W W ) 100 = 2x + 6x + 2x = 10x We are given that the total maximum percentage error in W is 30 % . 10x = 30 % x = 3 % The percentage error in the measurement of qua

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