Question

A quantity x is calculated by using the formula
$x=\frac{(p-q)}{r}$

The measured values are p = 9, q = 6, r = 0.5
Assume that the measurement errors in p, q and r are independent. The absolute maximum error in the measurement of each of the three quantities is $\epsilon .$ The absolute maximum error in the calculated value of x is

• A. $\epsilon$
• B. $2\epsilon$
• C. $3\epsilon$
• D. $16\epsilon$

Answer 1

The correct option is D $16\epsilon$

Given,
$\delta p=\delta q=\delta r=ϵ$

and p = 9, q = 6, r = 0.5

$x=\frac{(p-q)}{r}$

let, (p - q) = y

$\therefore x=\frac{y}{r}$

$maximumabsoluteerroriny=\delta y$

$\therefore \frac{\delta y}{y}=\frac{\delta (p-q)}{(p-q)}=(\frac{\delta p}{p-q}+\frac{\delta q}{p-q})$

$=(\frac{ϵ}{3}+\frac{ϵ}{3})=\frac{2ϵ}{3}$

$maximumabsoluteerrorinx=\delta x$

$\therefore \frac{\delta x}{x}=(\frac{\delta y}{y}+\frac{\delta r}{r})=(\frac{2ϵ}{3}+\frac{ϵ}{0.5})=\frac{8ϵ}{3}$

$\therefore \delta x=(\frac{8ϵ}{3}.x)=(\frac{8ϵ}{3}\times 6)=16ϵ$