Q12PE - College Physics (Urone)

Question

A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m  . What is its percent uncertainty?

Step-by-Step Solution

Answer

The Percent Uncertainty given case is  ${\mathrm{\delta }}_{\mathrm{L}}=0.025\%$.

Step 1: Defining concept of percentage uncertainty

Percentage uncertainty is just 100 percent related uncertainty. Since percentage uncertainty is also a measure of the same value, it has no units.

Given Data

Consider the given data as below.

Original Length=  $\mathrm{L}=20 \mathrm{m}$

Uncertainty in Length,  ${\mathrm{\delta }}_1=0.50 \mathrm{cm}=0.50\times {10}^{-2} \mathrm{m}$

Step 2: Defining percentage uncertainty formula

According to a mathematical formula,-

$$\begin{gathered} \mathrm{Percent} \mathrm{Uncertainty} =\frac{{\mathrm{\delta }}_1}{\mathrm{L}}\times 100\% \\ {\mathrm{\delta }}_{\mathrm{L}}=\frac{0.50\times {10}^{-2} \mathrm{m}}{20 \mathrm{m}}\times 100\% \\ =0.025\% \end{gathered}$$

Step 3: Stating conclusion

The Percent Uncertainty in the given case is  ${\mathrm{\delta }}_{\mathrm{L}}=0.025\%$.