In the formula `X=3YZ^(2), X` and `Z` have dimensions of capacitance and magnetic induction respectively. What are the dimensions of `Y` in `MKSQ` system?

Answer

`[M^(-3)L^(-2)T^(4)Q^(4)]`

Explanation

`[X]=["capacitance"]=[M^(-1)L^(-2)Q^(2)]` and
`[Z]=["Magnetic induction"]=[MT^(-1)Q^(-1)]`
Therefore
`[Y]=([X])/([Z]^(2))=([M^(-1)L^(-2)T^(2)Q^(2)])/([MT^(-1)Q^(-1)]^(2))=[M^(-3)L^(-2)T^(4)Q^(4)]`