If the velocity of light is taken as the unit of velocity and year as the unit of time find the unit of length?

Explanation

Dimensional formula for velocity is `v=[LT^(-1)]`
`n_(1)[L_(1)T_(1)^(-1)]=n_(2)[L_(2)T_(2)^(-1)]`
`L_(2)=((n_(1))/(n_(2)))((T_(1))/(T_(2)))^(-1)L_(1)`..i
Here `n_(1)` is the numerial value of velocity in the system where unit of length is `L_(1)` and that time is `T_(1)` and `n_(2)` is the numerical value of velocity in the system where unit of length is `L_(2)` and that of time is `T_(2)`.
`n_(1)=3xx10^(8)" "L_(1)=1m, " "T_(1)=1s`
`n_(2)=1" "L_(2)=?" "T_(2)=1"year"=365.25xx24xx60xx60s`
Substituting these values in equation (i)
`L_(2)=((3xx10^(8))/1)(1/(365.25xx24xx60xx60))^(-1)`(1)
`=3xx10^(8)xx365.25xx24xx60xx60=9.468xx10^(15)m`
This unit of length is called a light year.