Question

A physical quantity Pis related to four observables a, b, c and d as follows:
P=a^3b^2 (root under C d)
The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and2%,
respectively. What is the percentage error in the quantity P?​

Answer 1

$\huge{\underline{\tt{\red{Answer-}}}}$

Percentage error in P=13 %

Explanation:

given -$P= \dfrac{a^3 b^2}{\sqrt{cd}}$

Maximum fractional error in P is given by

$\dfrac {\Delta P}{P} = +-[3\dfrac{\Delta a}{a} + 2\dfrac{\Delta b}{b} + \dfrac{1}{2} \dfrac{\Delta c}{c} + \dfrac{\Delta d}{d}]$

On putting value:

$=0.13$

Percentage error in P=13 %