A physical quantity Q is found to depend on quantities a , b , c … - Vidyadip

MCQ

A physical quantity $Q$ is found to depend on quantities $a , b , c$ by the relation $Q =\frac{ a ^4 b^3}{ c ^2}$. The percentage error in $a, b$ and $c$ are $3 \%, 4 \%$ and $5 \%$ respectively. Then, the percentage error in $Q$ is :

A
66%
B
43%
C
34%
D
14%

✓

Answer

$ Q =\frac{ a ^4 b^3}{ c ^2}$
$\frac{\Delta Q }{ Q }=4 \frac{\Delta a }{ a }+3 \frac{\Delta b}{ b }+2 \frac{\Delta c }{ c }$
$ \frac{\Delta Q }{ Q } \times 100=4\left(\frac{\Delta a }{ a }\right. \times 100)+3\left(\frac{\Delta b}{ b } \times 100\right)+2\left(\frac{\Delta c }{ c } \times 100\right)$
$\%$ error in $Q =4 \times 3 \%+3 \times 4 \%+2 \times 5 \%$
$ =12 \%+12 \%+10 \%$
$ =34 \%$

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