Question

Question #15c33

Answer 1

This is what I get

Explanation:

Given that the day at the end of `1.0` century is `1.0\ ms` longer than the day at the start of the century.

`:.` in `88` centuries total increase on the last day of the century `=88xx1.0=88\ ms=8.8xx10^-2\ s`

Let us assume that the length of the day increases uniformly.

`implies` in `8800` years each day on an average was `(0+8.8xx10^-2)/2=4.4xx10^-2\ s` longer than the reference day at the beginning.

We know that a four-century period will be missing `3` of its `100` leap years. (Years `100, 200, 300` arn't leap years, whereas `400` is a leap year.)
So the average year has `365 + 97/400 = 365.2425\ days`

Therefore, cumulatively total effect
`="Average daily increase"xx"Number of days"`

`=4.4xx10^-2xx365.2425xx8800`
`=141421.9\ s~~39.28\ hr`