Question

The normal duration of physics practical period in Indian college is 100 minutes. Express this period in micro-century. 1micro-century = ${{10}^{-6}}\times 100$ years. How many micro-centuries did you sleep yesterday?

Answer 1

As a first step you could find the number of minutes in a year. Now from the given value of 1 micro-century you could find how many micro- centuries there are in one year and then combine the above two relations and get the normal duration of physics practical period (100 minutes) in micro-centuries. For the second part, assume that an average man sleeps for 8 hours and find the answer.

Complete step by step answer:
In the question we are given the normal duration of a physics practical period in Indian colleges that is 100minutes. We are asked to find this period in micro-century. We are given 1 micro-century as, $100\times {{10}^{-6}}$ years. In addition we are asked to find the time that we slept the previous day in micro-centuries.
As a first step let us find the number of minutes in a year.
To begin with, we have 60 minutes in an hour and we know that 24 hours makes a day.
So in a day we have, $60\times 24\min =1440\min$
Normally we have 365 days in a year (except for leap years with 366days). So, in a normal year we have,
$1440\times 365\min =525600\min$
Therefore, $1yr=525600\min$…………………….. (1)
We are given that,
1 micro-century = ${{10}^{-4}}yrs$
$\Rightarrow 1yr=\dfrac{1}{{{10}^{-4}}}={{10}^{4}}$ micro-centuries
From (1),
$\Rightarrow 525600\min ={{10}^{4}}$ micro-centuries ……………………. (2)
But we are asked to find 100 minutes in micro-centuries.
$\Rightarrow 100\min =\dfrac{100\times {{10}^{4}}}{525600}$ micro-centuries
$\Rightarrow 100\min =1.9$ micro-centuries
The normal duration of physics practical period in Indian college is found to be 1.9 micro-centuries.
Now we have to find how many micro-centuries we slept the previous day. Let us find this for an average person’s sleep cycle. Let us assume that normally a person sleeps for 8 hours.
From equation (2) we have,
$1hr=60\min =\dfrac{60\times {{10}^{4}}}{525600}$ micro-centuries
Now 8 hours in micro-centuries will be,
$8hrs=\dfrac{8\times 60\times {{10}^{4}}}{525600}$ micro-centuries
$\therefore 8hrs=9.13$ micro-centuries
Hence, we have found that an average man must have slept 9.13 micro-centuries the previous day.

Note:
Micro-century we know is the time period of one millionth of a century. This is not used as a standard unit of measurement but it is mostly used humorously for denoting the maximum duration of a lecture. The above calculation is done approximating the number of days in a century as 365 $\times$ 100, but we know that some of the years might be leap years, hence the number of days in a century is more than that.