Question

There is an unknown quantity $x=R\frac{l}{100 - l}$ , here $l$ is length $\left(\right.$ in $cm$ measured using a scale having least count of $1 \, cm$ . and $R \, $ is a quantity known accurately. Find the percentage error in measurement of $x$ for $l = 50 \text{cm}$ ?

• A. $1 \, \%$
• B. $6 \, \%$
• C. $2 \, \%$
• D. $4 \, \%$

Answer 1

Answer: (D)

$x=R\frac{\ell }{100 - \ell }$
$\frac{\Delta x}{x}=\frac{\Delta \ell }{\ell }+\frac{\Delta \ell }{100 - \ell }$
$\frac{\Delta x}{x}\times 100=\left(\frac{1}{50} + \frac{1}{50}\right)\times 100=4\%$