Question

A unit of time sometimes used in microscopic physics is the shake. One shake equals \[{10^{ - 8}}{\text{s}}\]. Are there more shakes in a second than there are seconds in a year?

Answer 1

Hint:We are asked whether there are more shakes in one second than there are seconds in one year. We are given the value of one shake in seconds, use this value to calculate how many shakes are there in one second. To calculate the value of seconds in one year, recall the number of days in one year, hours in one day, minutes in one hour and seconds in one minute. Using these values calculate how many seconds are there in one year. Then compare values and check whether there are more shakes in a second than there are seconds in a year.

Complete step by step answer:
Given, \[1\,{\text{shake}} = {10^{ - 8}}{\text{s}}\]. We are asked whether there are more shakes in a second than there are seconds in a year.First we need to check how many shakes are there in a second and then check how many seconds are there in a year. After that we will compare the two values.We are given,
\[1\,{\text{shake}} = {10^{ - 8}}{\text{s}}\]
If we divide the above equation both sides by \[{10^{ - 8}}\] we will have,
\[\dfrac{1}{{{{10}^{ - 8}}}}\,{\text{shake}} = 1\,{\text{s}}\]
\[ \Rightarrow {10^8}\,{\text{shake}} = 1\,{\text{s}}\]
\[ \Rightarrow 1\,{\text{s}} = {10^8}\,{\text{shake}}\]
We get that there are \[{10^8}\] shakes in a second.

We know that there \[{\text{365}}\] days in a year, that is
\[{\text{1yr}} = {\text{365 days}}\]
In one day we have \[{\text{24}}\]hours so, in \[{\text{365}}\] days we will have \[{\text{365}} \times 24\] hours, which means in one year we will have,
\[{\text{1yr}} = {\text{365}} \times 24\,{\text{hrs }}\]
In one hour we have \[{\text{60}}\] minutes so, in \[{\text{365}} \times 24\] hours we will have \[{\text{365}} \times 24 \times 60\] minutes, that is one year we will have,
\[{\text{1yr}} = {\text{365}} \times 24 \times 60\,\min \]

In one minute we have \[60\] seconds so, in \[{\text{365}} \times 24 \times 60\] minutes we will have \[{\text{365}} \times 24 \times 60 \times 60\] seconds, which means in one year we will have,
\[{\text{1yr}} = {\text{365}} \times 24 \times 60 \times 60\,{\text{s}}\]
\[ \Rightarrow {\text{1yr}} = {\text{31536000}}\,{\text{s}}\]
\[ \Rightarrow {\text{1yr}} = {\text{3}}{\text{.1536}} \times {\text{1}}{{\text{0}}^7}\,{\text{s}}\,\]
\[ \therefore {\text{1yr}} \approx {\text{1}}{{\text{0}}^7}\,{\text{s}}\]
We get there are \[{\text{1}}{{\text{0}}^7}\] seconds in one year.Now, if we compare the both results we get, one second has \[{10^8}\] shakes and one year has \[{\text{1}}{{\text{0}}^7}\] seconds.

Therefore, the answer will be yes, there are more shakes in a second than there are seconds in a year.

Note:There are three most commonly used units for time, these are second, minute and hour. Remember the conversion factor between these units, these are \[{\text{1}}\,{\text{hr}} = 60\,\min = 3600\,{\text{s}}\] and \[1\min = 60\,{\text{s}}\]. The SI and CGS unit of time is second.