Question

A new unit of length is chosen such that the speed of light in a vacuum is unity. What is the distance between the sun and the earth in terms of the new unit if the light takes $8\,$ min, and $20$ sec to cover this distance?
(A) $300$
(B) $400$
(C) $500$
(D) $600$

Answer 1

Earth is the third planet from the sun. It receives the light at a given time, converting it to seconds. Use the formula of the velocity of the light given below and substitute the known parameters like speed and the time taken to find the value of the distance between the sun and the earth.
Formula used:
The formula of the speed is given by
$v = \dfrac{d}{t}$
Where $v$ is the velocity of the light, $d$ is the distance between the sun and the earth and $t$ is the time taken by the light to travel.

Complete step-by-step solution:
It is given that the
Time is taken by the light to travel from the sun to the earth, $t = 8$ min $20$ sec.
Speed of the light in vacuum, $v = 1\,units$
Converting the time taken to the second, we get
$t = 8 \times 60 + 20$
By simplifying the above step, we get
$t = 500\,s$
Hence the time taken by the light to travel from the sun to the earth is calculated as $500\,s$
Using the formula of the speed,
$v = \dfrac{d}{t}$
BY rearranging the above formula, we get
$d = vt$
Substituting the velocity of the light and the time taken in the above rearranged formula, we get
$d = 1 \times 500$
Simplification of the above step, we get
$d = 500\,$ units.
Hence the distance between the sun and the earth is calculated as $500\,$ units.
Thus the option (C) is correct.

Note: The space filled between the sun and the Earth is the only vacuum. There is no medium like air, water, etc. Since it is given that the speed of light in a vacuum is unity, then the speed that the light must travel from the sun to the earth through the vacuum is also unity.