Question

A new unit of length is chosen such that the speed of light in vaccum is unity. What is the distance between the sun and the earth in terms of the new Unit if light takes 8 minutes and 20 second to cover the distance?

Answer 1

If the speed of light is taken as unity in vacuum, then 1 unit of that length will be equal to 3 Х 108 m. (As speed of light in vacuum is 3 Х 108ms-1)

Let us write this in the following form:
1 c = 3 Х 108 m; where ‘c’ is the new unit of length. This will be our conversion equation to solve the question.

Light from the sun reaches earth in 8 min and 20 s, i.e. (8 Х 60 + 20) s = 500 s.

So, the distance travelled by light to reach the earth is L (say),
L = Speed of light in vacuum Х time taken
Or, L = 3 Х 108 ms-1 Х 500 s = 500 Х 3 Х 108 m

Now, using the conversion equation,
L = 500 Х (1 c) = 500 c

Hence, the distance between the sun and the earth according to the new unit is 500 c.