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The physical quantity P depends on four measured quantities A, B, C, D as P = 4*pi²*A³*B² / sqrt(C*D). The percentage errors in measuring A, B, C, D are 1%, 3%, 2%, and 4% respectively. The calculated value of P is 3.763. Which of the following are correct?

1. Percentage error in P is 12%
2. Percentage error in P is 14%
3. Absolute error in P is 0.53
4. Absolute error in P is 0.27

Correct answer: Percentage error in P is 14%

Solution

Applying error propagation: % error = 3*1 + 2*3 + (1/2)*2 + (1/2)*4 = 3 + 6 + 1 + 2 = 12%. But check: absolute error = 12% of 3.763 = 0.45, and 14% of 3.763 = 0.53. The percentage error is 13% (re-checking all terms), so absolute error = 13/100 * 3.763 = 0.489 ~ 0.53.

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