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1.Units, Dimensions and Measurement
medium
A physical quantity $'x'$ is calculated from the relation $x = \frac{{{a^2}{b^3}}}{{c\sqrt d }}$ in $a$,$b$,$c$ and $d$ are $2\%$, $1 \%$, $3\%$ and $4\%$ respectively, what is the percentage error in $x$.
A
$ \pm 11\%$
B
$ \pm 13\%$
C
$ \pm 12\%$
D
$ \pm 14\%$
Solution
$A =\frac{ a ^{2} b ^{3}}{ c \sqrt{ d }}$
$\frac{\Delta a }{ a } \times 100=1 \%,$$ \frac{\Delta b }{ b } \times 100=3 \%,$$ \frac{\Delta c }{ c } \times 100=2 \%$ and $\frac{\Delta d }{ d } \times 100=2 \%$
$\frac{\Delta A }{ A } \times 100=2 \frac{\Delta a }{ a } \times 100+3 \frac{\Delta b }{ b } \times 100+$$\frac{\Delta c }{ c } \times 100+\frac{1}{2} \times \frac{\Delta d }{ d } \times 100$
$\frac{\Delta A }{ A } \times 100=2 \times 2+3 \times 1+3+\frac{1}{2} \times 4=12 \%$
Standard 11
Physics
