A new unit ($\alpha$) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $\alpha$ units if light takes $6$ min. $40$ s to cover this distance?
Answer: (B) $400\alpha$
Concept. A unit of length can be defined through a speed: here one "$\alpha$" is the distance light covers in one second. Then a distance in $\alpha$ units is simply the light travel time in seconds.
Step 1. Light travel time in seconds.
$$t=6\ \text{min}\ 40\ \text{s}=6\times60+40=400\ \text{s}$$
Step 2. Distance. In $1$ s light covers $1\alpha$, so in $400$ s it covers
$$d=c\,t=400\times(c\times1\ \text{s})=400\alpha$$
Answer. $400\alpha$ (Option B). In metres this is $400\times3\times10^8=1.2\times10^{11}$ m.
Solution by Sreeraj P, M.Sc Physics
