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A physical quantity z depends on four observables a , b , c and d , as z = a 2 b 2 / 3 c d 3 . The percentage of error in the measurement of a , b , c and d are 2 % , 1 . 5 % , 4 % and 2 . 5 % respectively. The percentage of error in z is :

Options

  1. A12 . 25 %
  2. B16 . 5 %
  3. C13 . 5 %
  4. D14 . 5 %

Correct answer

D. 14 . 5 %

Step-by-step solution

Δ t t = 2 Δ a a + 2 3 Δ b b + 1 2 Δ c c + 3 Δ d d = 2 × 2 + 2 3 × 1 . 5 + 1 2 × 4 + 3 × 2 . 5 = 4 + 1 + 2 + 7 . 5 = 14 . 5 %

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