Q14P - Fundamentals Of Physics

Question

Question: A lecture period (50 min) is close to 1 microcentury. (a) How long is a microcentury in minutes? (b) Using 

, $\mathit{p}\mathit{e}\mathit{r}\mathit{c}\mathit{e}\mathit{n}\mathit{t}\mathit{a}\mathit{g}\mathit{e}\mathbf{ }\mathit{d}\mathit{i}\mathit{f}\mathit{f}\mathit{e}\mathit{r}\mathit{e}\mathit{n}\mathit{c}\mathit{e}\mathbf{=}\left(\frac{actual -approximation}{actual}\right)\mathbf{\times }\mathbf{100}$

find the percentage difference from the approximation.

Step-by-Step Solution

Answer

Answer

 

1. Duration of 1 microcentury is .
2. The percentage difference in the actual and approximate duration of the microcentury is 9%.

 

Step 1: Given data

The lecture period of 50 min is close to a microcentury.

Step 2: Understanding the duration of micro century

A time period of a millionth of a century, equal to 52 minutes and 35.7 seconds

Step 3: (a) Determination of the duration of micro century

Calculate the duration of 1 microcentury in minutes as follows:

 $$\begin{gathered} 1 microcentuary ={10}^6 century\left(\frac{100y}{1 century}\right)\left(\frac{365 day}{1 y}\right)\left(\frac{24 hr}{1 day}\right)\left(\frac{60min}{1 hr}\right) \\ = 52.6 min \end{gathered}$$ 

Thus, the duration of 1 micro century in minutes is 52.6 min .

Step 4: (b) Determination of the percentage difference

The percentage difference can be calculated as follows:

 $$\begin{gathered} percentage difference=\left(\frac{\mathrm{actual} -\mathrm{approximation}}{\mathrm{actual}}\right)\times 100 \\ =\left(\frac{52.6-50}{52.6}\right)\times 100 \\ =0.049\times 100 \\ =4.9\% \end{gathered}$$

 

Thus, the percentage difference is 4.9%.