Question

In an experiment four quantities a, b, c and d are measured with percentage error $1$ %, $2$%, $3$% and $4$% respectively. Quantity P is calculated as follows:
$P=\frac{a{b}^2}{\sqrt{c{d}^3}}$
Percentage error is P is

• A. $4$%
• B. $7$%
• C. $9$%
• D. $10$%

Answer 1

The correct option is D $10$%

Quantity $P$ is calculated as follow $P=\frac{a{b}^2}{\sqrt{c{d}^3}}$

Formula of % error should be,

% error in $P=3\times$%error in $a+2\times$% error in $b+$%error in $c+$% error in d

Given,

% error in $a=1$%

% error in $b=2$%

% error in $c=3$%

% error in $d=4$%

Hence,

% error in $P=3\times 1+2\times 2+3+4$

$=3$%-$4$%+$3$%+$4$%

$=10$%

$\therefore$ Option $D$ is correct answer.