A physical quantity z depends on four observables a, b, c and d ,… - Vidyadip

MCQ

A physical quantity $z$ depends on four observables $a,$ $b,$ $c$ and $d ,$ as $z =\frac{ a ^{2} b ^{\frac{2}{3}}}{\sqrt{ c } d ^{3}} .$ The percentage of error in the measurement of $a, b, c$ and $d$ are $2 \%, 1.5 \%, 4 \%$ and $2.5 \%$ respectively. The percentage of error in $z$ is$......\%$

A
$12.5$
✓
$14.5$
C
$16.5$
D
$13.5$

✓

Answer

Correct option: B.

$14.5$

b
$\frac{\Delta Z}{Z}=\frac{2 \Delta a }{ a }+\frac{2}{3} \frac{\Delta b }{ b }+\frac{1}{2} \frac{\Delta c }{ c }+\frac{3 \Delta d }{ d }=14.5 \%$

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