Answer

Verified

437.1k+ views

**Hint:**First, we will find the total time difference between the start of the 1st century and the end of the 20th century. Next, we will find the average increase in the length of the day by taking the average of the initial time difference and the final time difference. Finally, we will be multiplying the average length of the day to the total number of days to find the net total time difference and then by converting from seconds to hours.

**Complete step-by-step solution**Here it is given that the length of the day increases by 0.001 second or 1 millisecond per century. We have to find the time difference after 20 centuries.

We need to find the total difference in time between the beginning of the first century and the end of the 20th century initially.

Total difference = $\left( \dfrac{0.001\text{s}}{1\,\text{century}} \right)\cdot \left( \dfrac{20\,\text{centuries}}{1} \right)=0.02\text{s}$

Since the time difference is increasing uniformly, let us now find the average increase in the length of the day between the first century and the end of the 20th century.

Average $=\dfrac{{{D}_{i}}+{{D}_{f}}}{2}$, where ${{D}_{i}}$ = initial time difference, ${{D}_{f}}$ = final time difference

Average $=\dfrac{0+0.02}{2}$

$\begin{align}

& =\dfrac{0.02}{2} \\

& =0.01 \\

\end{align}$

Therefore, the average increase in the length of the day is 0.01s

Now, finally let us find the total time difference, which is all the time displacement that occurs throughout the 20 centuries added up is equal to T.

Here, we get

$\text{T}\,\text{=}\,{{D}_{avg}}\cdot n$, where ${{D}_{avg}}$ is the average increase in the length of the day and $n$ is the total number of days.

$\begin{align}

& \text{T}\,\text{=}\,\left( \dfrac{0.01\text{s}}{\text{1 day}} \right)\cdot \left( \dfrac{365.25}{1\,\text{year}} \right)\cdot \left( \dfrac{2000\,\text{years}}{1} \right) \\

& =7305

\end{align}$

We got the total time difference as 7305 seconds, but the question has been asked in hours, therefore we will divide total time difference (seconds) by $60\times 60$ to get the obtained time difference in hours.

We get,

$\begin{align}

& \text{T =}\dfrac{7305}{60\times 60} \\

& =\dfrac{7305}{3600} \\

& =2.029

\end{align}$

The closest number to the obtained answer is 2.1 hours.

**Hence, the net effect on the measure of time over 20 centuries is 2.1 hours**

**Note:**In this question, in the final step, we took the total number of days in a year is 365.25 as an average because in every leap year we have 366 days and we know that in 1 century there are 100 years, therefore, for 20 centuries there will be 2000 years. Also, note that 1ms = 0.001s.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

The polyarch xylem is found in case of a Monocot leaf class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Change the following sentences into negative and interrogative class 10 english CBSE

Casparian strips are present in of the root A Epiblema class 12 biology CBSE