Chapter 1, Problem 50GP

To determine

To Find: The accuracy of the watch in percentage.

Answer to Problem 50GP

  $\pm 2.54\times {10}^{-5}\%$

Explanation of Solution

Given:

Gain or loss of the watch is not more than $8\text{ s}$ in a year.

Formula used:

Uncertainty percentage is,

  $\%\text{ = }\frac{\text{amount of uncertainty }}{\text{ maximum value}}\times 100\%$

Calculation:

Convert one year in to seconds

  $\begin{array}{l}1\text{year}=1\times 365\times \text{24}\times \text{3600 s}\\ 1\text{year}=3.154\times {10}^7\text{ s}\end{array}$

Percent of uncertainty can be calculated as:

  $\begin{array}{c}\%\text{ = }\frac{\pm 8}{3.154\times {10}^7}\times 100\\ \text{= ±}2.536\times {10}^{-5}\%\\ \%\approx \pm 2.54\times {10}^{-5}\%\end{array}$

Conclusion:

Therefore, $\pm 2.54\times {10}^{-5}\%$ is the percent of uncertainty of the watch.