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 min and 20 s to cover this distance ?

The correct option is 500 new units of length.

Step 1: Understand the new unit system
According to the question, a new unit of length is chosen such that the speed of light in vacuum is unity. Let the new unit of length be represented as "nu".
Therefore, the speed of light ($c$) in the new unit system is:
$c=1\text{nu/s}$

Step 2: Convert the time taken into seconds
The time taken ($t$) by light to travel from the sun to the earth is given as 8 minutes and 20 seconds.
We know that:
$1\text{minute}=60\text{seconds}$
So, converting the entire duration into seconds:
$t=(8\times 60)\text{s}+20\text{s}$
$t=480\text{s}+20\text{s}$
$t=500\text{s}$

Step 3: Calculate the distance
The formula relating distance ($d$), speed ($v$), and time ($t$) is:
$d=v\times t$
Here, the speed of light is $v=c=1\text{nu/s}$, and the time is $t=500\text{s}$.
Substituting these values into the formula:
$d=1\text{nu/s}\times 500\text{s}$
$d=500\text{new units of length}$

Thus, the distance between the sun and the earth in terms of the new unit is 500 new units of length.