A physical quantity A is related to four observable a,b,c and d a… - Vidyadip

MCQ

A physical quantity $A$ is related to four observable $a,b,c$ and $d$ as follows, $A = \frac{{{a^2}{b^3}}}{{c\sqrt d }}$, the percentage errors of measurement in $a,b,c$ and $d$ are $1\%,3\%,2\% $ and $2\% $ respectively. What is the percentage error in the quantity $A$ ......... $\%$

A
$12$
B
$7$
C
$5$
✓
$14$

✓

Answer

Correct option: D.

$14$

d
$A =\frac{ a ^{2} b ^{3}}{ c \sqrt{ d }}$

$\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$

$\frac{\Delta A }{ A } \times 100=2 \times 1+3 \times 3+2+\frac{1}{2} \times 2=14 \%$

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