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

Explanation

(i) Being a force, frictional force can be given by the relation,
Frictional force = Mass `xx` Acceleration
`therefore` [Frictional force] = [Mass] [Retardation]
= `[M][LT^(-2)]`
= `[MLT^(-2)]`
(ii) Charge = Current `xx` 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^(0)L^(0)T^(0)]`
Above equation shows that refractive index does not have any dimensions. Such quantities are known as dimensionless quantities.