Question

if R=a^2√b/c^4d and percentage error in measurement of a,b,c and d are 0.1%,0.2%,0.3%and 0.4% respectively, then the maximum pecentage error in R is
(a) 1.9%
(b) 3.1%
(c) 2.9%​

Answer 1

Given :

$\bigstar\bf\:R=\dfrac{a^2\sqrt{b}}{c^4d}$

▪ Percentage error in a = 0.1%

▪ Percentage error in b = 0.2%

▪ Percentage error in c = 0.3%

▪ Percentage error in d = 0.4%

To Find :

▪ Maximum percentage error in R.

Calculation :

➡ Maximum percentage error in R is givem by

$\bigstar\:\underline{\boxed{\bf{\purple{\%\dfrac{\Delta R}{R}=\%\dfrac{2\Delta a}{a}+\%\dfrac{\Delta b}{2b}+\%\dfrac{4\Delta c}{c}+\%\dfrac{\Delta d}{d}}}}}\\ \\ \implies\rm\red{\%\dfrac{\Delta a}{a}=0.1\%}\\ \\ \implies\rm\blue{\%\dfrac{\Delta b}{b}=0.2\%}\\ \\ \implies\rm\green{\%\dfrac{\Delta c}{c}=0.3\%}\\ \\ \implies\rm\orange{\%\dfrac{\Delta d}{d}=0.4\%}\\ \\ \longrightarrow\sf\:\%\dfrac{\Delta R}{R}=2(0.1\%)+\dfrac{(0.2\%)}{2}+4(0.3\%)+(0.4\%)\\ \\ \longrightarrow\sf\:\%\dfrac{\Delta R}{R}=(0.2\%)+(0.1\%)+(1.2\%)+(0.4\%)\\ \\ \longrightarrow\underline{\boxed{\bf{\purple{\%\dfrac{\Delta R}{R}=1.9\%}}}}$

Answer 2

Answer:

1.9 percent

Explanation:

1.9 percent is the ans