A physical quantity P is related to four observations a, b, c and d as follows: P=a^3 b^2/c√d. The percentage errors of measureme…

Question

A physical quantity P is related to four observations a, b, c and d as follows: P=a^3 b^2/c√d. The percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 4% respectively. The percentage error in the quantity P is:

1. A. 10%
2. B. 2%
3. C. 13% (Correct answer)
4. D. 15%

Correct Answer

Option C — 13%

Detailed Solution & Explanation

The correct answer is 13%.

Key Points

• For $P=\dfrac{a^3 b^2}{c\sqrt{d}}$, the maximum percentage error adds up each contribution weighted by its power.
• $\dfrac{\Delta P}{P}\times100=3(1\%)+2(3\%)+1(2\%)+\dfrac{1}{2}(4\%)$.
• $=3+6+2+2=13\%$.