Physics

# 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?

##### SOLUTION

Dfractional error in P is

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

$\dfrac{\Delta P}{P}=\left[ \dfrac{3}{100}+\dfrac{9}{100}+\dfrac{2}{100}+\dfrac{2}{100} \right]$

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

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

It is given that $P=3.763$

So the round off value is 3.8

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Subjective Medium Published on 18th 08, 2020
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