A physical quantity P is given as P=a^2 b^3 c d The percentage er… - Vidyadip

MCQ

A physical quantity $P$ is given as $P=\frac{a^2 b^3}{c \sqrt{d}}$ The percentage error in the measurement of $a, b, c$ and $d$ are $1 \%, 2 \%, 3 \%$ and $4 \%$ respectively. The percentage error in the measurement of quantity $P$ will be $.......\%$

✓
$13$
B
$14$
C
$12$
D
$16$

✓

Answer

Correct option: A.

$13$

a
$\frac{\Delta P }{ P } \times 100 \%=\left(2 \frac{\Delta a }{ a }+3 \frac{\Delta b }{ b }+\frac{\Delta c }{ c }+\frac{1}{2} \frac{\Delta d }{ d }\right) \times 100 \%$

$=2(1 \%)+3(2 \%)+3 \%+\frac{1}{2} \times 4 \%=13 \%$

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