Question

A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes $8\text{min}$ ⁡⁡⁡and $20s$ to cover this distance?

Answer 1

Given: According to the problem, speed of light in

vacuum, $c=1$ new unit of length $s^{-1}$
Time taken by light to cover distance between sun and earth
$t=8\text{min}20s=500s$

$\therefore$ Distance between sun and earth (in terms of new unit)
$=c\times t=1$ (new unit of length $\times 500s$)

$=500$ new units of length