Question

Find the dimensions of the following physical quantities .
(i)Frictional force , (ii)Charge , (iii)Refractive index

Answer 1

(i)Being a force, frictional force can be given by the relation, Frictional force = Mass x Acceteration
`therefore` [Frictional force] = [Mass ] [Retardation]
`=[M][LT^(-2)]`
`=[MLT^(-2)]`
(ii)Charge = Current x time
[Charge ] = [Current ] [ Time]
=[AT]
(iii)Refractive index , `mu="Speed of light in vacuum"/"Speed of light in medium "`
`[mu]=([LT^(-1)])/([LT^(-1)])`
`[mu]=[M^0L^0T^0]`
Above equation shows that refractive index does not have any dimensions. Such quantities are known as dimensionless quantities.