Question

A physical quantity P is related to four observables a, b, c, d as follows: P = $P=\frac{a^3{b}^2}{(\sqrt{c},d)}$ The percentage errors in the measurement of a, b, c and d are $1\%3\%4\%and2\%$ respectively. The percentage error in the quantity P is

• A. 7$\%$
• B. 9$\%$
• C. 11$\%$
• D. 13$\%$

Answer 1

The correct option is D 13$\%$

P = $a^3{b}^2.c^{-\frac{1}{2}}.d^{-1}\left|\frac{\Delta P}{P}\right|=3\left|\left(\frac{\Delta a}{a}\right)\right|+2\left|\left(\frac{\Delta b}{b}\right)\right|+\frac{1}{2}\left|\frac{\Delta c}{c}\right|+\left|\frac{\Delta d}{d}\right|\Rightarrow \text{Percentage error in P}=3\left(1\%\right)+2\left(3\%\right)+\frac{1}{2}\left(4\%\right)+2\%=(3+6+2+2)\%=13\%$