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Question: A physical quantity A is related to four observables a, b, c and d as following A = \(\frac{a^{2}b^{...

A physical quantity A is related to four observables a, b, c and d as following A = a2b3cd\frac{a^{2}b^{3}}{c\sqrt{d}}

The percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity A?

A

12%

B

7%

C

5%

D

14%

Answer

14%

Explanation

Solution

ΔAA=2(Δaa)+3(Δbb)+1(Δcc)+12(Δdd)\frac{\Delta A}{A} = 2\left( \frac{\Delta a}{a} \right) + 3\left( \frac{\Delta b}{b} \right) + 1\left( \frac{\Delta c}{c} \right) + \frac{1}{2}\left( \frac{\Delta d}{d} \right)