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1.Units, Dimensions and Measurement
easy
If $Z=\frac{A^{2} B^{3}}{C^{4}}$, then the relative error in $Z$ will be
A
$\frac{\Delta A }{ A }+\frac{\Delta B }{ B }+\frac{\Delta C }{ C }$
B
$\frac{2 \Delta A }{ A }+\frac{3 \Delta B }{ B }-\frac{4 \Delta C }{ C }$
C
$\frac{2 \Delta A }{ A }+\frac{3 \Delta B }{ B }+\frac{4 \Delta C }{ C }$
D
$\frac{\Delta A }{ A }+\frac{\Delta B }{ B }-\frac{\Delta C }{ C }$
(JEE MAIN-2022)
Solution
$Z=\frac{A^{2} B^{3}}{C^{4}}$
In case of error
$\frac{ dZ }{ Z }=\frac{2 d A}{ A }+\frac{3 dB }{ B }+\frac{4 dC }{ C }$
$\frac{\Delta Z }{ Z }=\frac{2 \Delta A }{ A }+\frac{3 \Delta B }{ B }+\frac{4 \Delta C }{ C }$
Standard 11
Physics
