Question

Let $x=\left[\frac{a^2{b}^2}{c}\right]$ be the physical quantity. If the percentage error in the measurement of physical quantities a, b and c is $2,3and4$ percent respectively then percentage error in the measurement of x is

• A. $7\%$
• B. $14\%$
• C. $21\%$
• D. $28\%$

Answer 1

Answer: (B)

$14\%$

$x=\frac{a^2{b}^2}{c}$

$⟹\frac{\Delta x}{x}=2\frac{\Delta a}{a}+2\frac{\Delta b}{b}+\frac{\Delta c}{c}$

$⟹\frac{\Delta x}{x}=2\times 2+2\times 3+4$

$⟹\frac{\Delta x}{x}=14\%$

Hence, answer is option-(B).