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 the termsof newunit ,if light takes 8minutes and 20 seconds to cover this distance?

Answer 1

$$\begin{gathered} \mathrm{Time}\left(\mathrm{t}\right)=8\mathrm{minute}20\mathrm{second}=500\mathrm{s} \\ \mathrm{Velocity}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{vacuum}\left(\mathrm{c}\right)=1\mathrm{new}\mathrm{unit}\mathrm{of}\mathrm{length}{\mathrm{s}}^{-1} \\ \mathrm{Distance}\mathrm{between}\mathrm{sun}\mathrm{and}\mathrm{earth}, \\ \mathrm{X}=\mathrm{c}\times \mathrm{t} \\ \mathrm{X}=1\mathrm{new}\mathrm{unit}\mathrm{of}\mathrm{length}{\mathrm{s}}^{-1}\times 500\mathrm{s} \\ \mathrm{X}=500\mathrm{new}\mathrm{unit}\mathrm{of}\mathrm{length} \end{gathered}$$