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In the measurement of a physical quantity X= A^2 B C^ 1 / 3 D^3 . The percentage errors introduced in the measurements of the quantities A, B, C , and D are 2 %, 2 %, 4 % and 5 % , respectively. Then, the minimum amount of percentage error in the measurement of X is contributed by

Options

  1. AA
  2. BB
  3. CC
  4. DD

Correct answer

C. C

Step-by-step solution

aligned & x= A^2 B C^ 1 / 3 D^3 & % error in x, & x x =2 A A + B B + 1 3 C C + 3 D D & 2 ( A A 100 % )+ ( B B 100 % ) & + 1 3 ( C C 100 % )+3 ( D D 100 % ) aligned Minimum percentage error = 1 3 ( C C 100 % )= 1 3 4=1.1 %

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