Answer

Verified

403.2k+ 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

The base of a right prism is a pentagon whose sides class 10 maths CBSE

A die is thrown Find the probability that the number class 10 maths CBSE

A mans age is six times the age of his son In six years class 10 maths CBSE

A started a business with Rs 21000 and is joined afterwards class 10 maths CBSE

Aasifbhai bought a refrigerator at Rs 10000 After some class 10 maths CBSE

Give a brief history of the mathematician Pythagoras class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Name 10 Living and Non living things class 9 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

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

Write a letter to the principal requesting him to grant class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail