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1.Units, Dimensions and Measurement
easy
For $z=a^{2} x^{3} y^{\frac{1}{2}}$, where $a$ is a constant. If percentage error in measurement of $x$ and $y$ are $4 \%$ and $12 \%$, respectively, then the percentage error for $z$ will be $........... \%$
A$18$
B$188$
C$78$
D$15$
(JEE MAIN-2022)
Solution
$z = a ^{2} x ^{3} y ^{1 / 2}$
$\frac{\Delta z }{ z }=\frac{2 \Delta a }{ a }+\frac{3 \Delta x }{ x }+\frac{1}{2}\frac{\Delta y }{ y }$
$a$ is constant
$\frac{\Delta z}{z} \times 100=3(4 \%)+\frac{1}{2}(12 \%)=18%$
$\frac{\Delta z }{ z }=\frac{2 \Delta a }{ a }+\frac{3 \Delta x }{ x }+\frac{1}{2}\frac{\Delta y }{ y }$
$a$ is constant
$\frac{\Delta z}{z} \times 100=3(4 \%)+\frac{1}{2}(12 \%)=18%$
Standard 11
Physics
