Q20PE - College Physics (Urone)

Question

(a) A person’s blood pressure is measured to be $\mathbf{120}\mathbf{\pm }\mathbf{2}\mathbf{ }\mathbf{mm}\mathbf{ }\mathbf{Hg}$. What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of  80  mm  Hg?

Step-by-Step Solution

Answer

1. The measured blood pressure has a percent uncertainty of  2.00%.
2. The uncertainty in blood pressure is  1 mm Hg.

Step 1: Definition of percentage uncertainty

Uncertainty as a percentage is just relative uncertainty multiplied by 100. The percent uncertainty likewise lacks units since it is a ratio of comparable values.

Given Data:

Consider the given data as below.

Blood pressure is measured to be  $\mathrm{A}=120\pm 2 \mathrm{mm} \mathrm{Hg}$.

The uncertainty of blood pressure is  $\mathrm{\delta } \mathrm{A}=2 \mathrm{mm} \mathrm{Hg}$.

Step 2: (a) Defining the percentage uncertainty

The percentage uncertainty is defined by,

$$\begin{gathered} \mathrm{Percent} \mathrm{Uncertainty}=\frac{\mathrm{\delta A}}{\mathrm{A}}\times 100\% \\ =\frac{2 \mathrm{mm} \mathrm{Hg}}{120 \mathrm{mm} \mathrm{Hg}}\times 100\% \\ =1.67\% \\ : 2.00\% \end{gathered}$$

Hence, the measured blood pressure has a percent uncertainty of  2.00%.

Step 3: (b) Calculating the percentage uncertainty in blood pressure

The percent uncertainty in measured blood pressure of  80 mm Hg.

The uncertainty in the blood pressure can be calculated as follows:

$\mathrm{Percent} \mathrm{Uncertainty}=\frac{\mathrm{\delta A}}{\mathrm{A}}\times 100\%$

Substitute known values in the above equation.

$$\begin{gathered} 1.67\%=\frac{\mathrm{\delta A}}{80 \mathrm{mm} \mathrm{Hg}}\times 100\% \\ \mathrm{\delta A}=\frac{1.67\times 80}{100} \\ =1.336 \\ : 1 \mathrm{mm} \mathrm{Hg} \end{gathered}$$

Hence, the uncertainty in blood pressure is  1 mm Hg.