Question

A physical quanity $P$ is releated to four observation $a,b,c$ and $d$ as follows $P=a^3{b}^3/\surd cd$The percentage errors of measurement in $a,b,c$ and $1\%,3\%,4\%$ and $2\%$ repectively. What is the percentage erros in quanity $P$? If the value of $P$. Calculated using the above relations turns out to +ve $3.763$, to what value you should round off the result?

Answer 1

Dfractional error in P is

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

$\frac{\Delta P}{P}=[\frac{3}{100}+\frac{9}{100}+\frac{2}{100}+\frac{2}{100}]$

$\frac{\Delta P}{P}=\frac{16}{100}=0.16$

Percentage error on $P=\frac{\Delta P}{P}\times 100=16$%

It is given that $P=3.763$

So the round off value is 3.8