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Accuracy and Precision

A physical qu...

Question

A physical quantity P is related to four measurables a, b, c and d by the formula $P = \frac{a^{3} b^{2}}{\sqrt{c} d}$ . The percentage errors in the measurement of a, b, c and d are 1%, 3%, 4% and 2% respectively. What is the percentage error in the quantity P ?

A

13%

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B

12%

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C

10%

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D

8%

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Solution

The correct option is A 13%
The percentage error in P $= 3 \times$ the percentage error in a + $2 \times$ the percentage error in b + $\frac{1}{2} \times$ the percentage error in c + the percentage error in d

Thus, the percentage error in P $= 3 + 6 + 2 + 2 = 13 %$

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