Question

What is the distance between the sun and the earth in terms of a new unit of length such that the speed of light in vacuum is unity? Given light takes $8$ minutes and $20$ seconds to cover the distance between the sun and the earth?

• A. 500
• B. 300
• C. 200
• D. 100

Answer 1

Answer: (A)

The speed of light in vacuum $\left(c\right)=1$ (new unit of length $s^{-1}$)
Time taken by light to reach the earth
$t=8\,min+20\,s$
$\Rightarrow t=\left(8 \times 60 + 20 s\right)=500\,s$
$\therefore $ Distance between the sun and the earth = Speed of light $\times$ Time
$x=c\times t$
$\Rightarrow x=1$ (new unit of length $s^{-1}$) $\times 500\,s$
$\Rightarrow x=500$ new unit of length