Question

A physical quantity $A$ is related to four observable $a,b,c$ and $d$ as follows, $A=\frac{a^2{b}^3}{c\sqrt{d}}$, the percentage errors of measurement in $a,b,c$ and $d$ are $1$%, $3$%, $2$% and $2$% respectively. What is the percentage error in the quantity $A$?

• A. $12$%
• B. $7$%
• C. $5$%
• D. $14$%

Answer 1

Answer: (D)

$14$%

The given physical quantity $A=\frac{a^2{b}^3}{c\sqrt{d}}$

Given : $\frac{\Delta a}{a}\times 100=1$%, $\frac{\Delta b}{b}\times 100=3$%, $\frac{\Delta c}{c}\times 100=2$% and $\frac{\Delta d}{d}\times 100=2$%

Percentage error in A, $\frac{\Delta A}{A}\times 100=$ $2\frac{\Delta a}{a}\times 100$ $+3\frac{\Delta b}{b}\times 100$ $+\frac{\Delta c}{c}\times 100+\frac{1}{2}\times \frac{\Delta d}{d}\times 100$

$⟹\frac{\Delta A}{A}\times 100=2\times 1+3\times 3+2+\frac{1}{2}\times 2=14$ %