Question

How many times will light travel around the Earth in one second?
A. $7$times
B. $5$ times
C. $3$ times
D. $9$ times

Answer 1

The time required to travel a particular distance with a speed $v$ will be $t = \dfrac{d}{v}$, where $d$ is the distance to be travelled. The distance will be the circumference of the earth. Find the time required to cover the circumference of the earth, then using the available data, find how many times the light can travel around the Earth in one second.

Complete step by step answer:
The time required to travel around the earth by the light will be $t = \dfrac{{2\pi R}}{c}$,
$t = \dfrac{{2\pi \times 6400000}}{{3 \times {{10}^8}}} \\\ \implies t = 0.134s \\\$
Therefore, the time required by the light to cover the circumference of the earth is $0.134s$.
Let $m$be the revolutions made by light around earth in $1s$. Think of this in an opposite way. To complete one revolution, it requires $0.134s$. Then, to complete $m$ revolutions it will require $0.134$ times $m$ seconds, that is $0.134m$ $s$. And we have said that for $m$ revolutions, the time is $1s$. Therefore,
$0.134m = 1 \\\ \implies m = \dfrac{1}{{0.134}} \\\ \implies m = 7.462 \\\$
Hence, the number of revolutions made by light around earth in $1s$ is $7.462$. It indicates that the light will travel $7.642$ times around the earth in $1s$. The most appropriate answer is $7$ times

So, the correct answer is “Option A”.

Note:
Here we have not considered the non-uniformity of the earth. Earth is not exactly spherical. It consists of a huge amount of water and of various types of rocks. Due to the rotation of the earth around its axis, the water and rocks are displaced making the earth to spread and flatten out. Hence the circumference is changed, longer for the equator and shorter for the prime meridian. But actually it does not matter which circumference is considered because the difference between the two values is not much. It can be neglected.