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

If the velocity of light is taken as the unit of velocity and year as

1.	If the velocity of light is taken as the unit of velocity and year as the unit of time find the unit of length?
Answer» SOLUTION :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.