Physics

# A physical quantity $x$ is calculated from the relation $x={ a }^{ 3 }{ b }^{ 2 }/\sqrt { cd }$. Calculate percentage error in $x$, if $a,b,c$ and $d$ are measured respectively with an error of $1\%$, $3\%$, $4\%$ and $2\%$.

$12\%$.

##### SOLUTION
Given $x = \dfrac{a^3b^2}{c^{1/2}d^{1/2}}$
On taking log and differentiating, we get

$\dfrac{\Delta x}{x}$ $=3\dfrac{\Delta a}{a}$  $+2\dfrac{\Delta b}{b}$  $+(\dfrac{1}{2})\dfrac{\Delta c}{c}$  $+(\dfrac{1}{2})\dfrac{\Delta d}{d}$

$\Rightarrow$ Percentage error in $x= 3(1)+2(3)+\dfrac{1}{2}(4)+\dfrac{1}{2}(2) = 12\%$

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Single Correct Medium Published on 18th 08, 2020
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