Question

A physical quantity P is repleted to four observed a,b,c,d as follows: $P=\frac{a^3{b}^2}{(\sqrt{c}.d)}$ The percentage errors in the measurement of a,b,c and d are $1\%3\%,4\%$ and $2\%$ respectively. The percentage error in the quantity P is

• A. $7\%$
• B. $9\%$
• C. $11\%$
• D. $13\%$

Answer 1

The correct option is D $13\%$

$P=\frac{a^3{b}^2}{\sqrt{cd}}$

$\frac{\Delta P}{P}=\frac{3\Delta a}{a}+\frac{2\Delta b}{b}+\frac{1}{2}\frac{\Delta c}{c}+\frac{\Delta d}{d}$

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

$=3\times 1+2\times 3+\frac{1}{2}\times 4+2$

$=3+6+2+2=13$%

Percentage error $=13$%