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

Options

A. `[M^(2)L^(-2)T^(3)Q^(4)]`
B. `[M^(-3)L^(-2)T^(4)Q^(4)]`
C. `[M^(-2)L^(-2)T^(4)Q^(3)]`
D. `[M^(-3)L^(-1)T^(3)Q^(4)]`

Answer

b

Explanation

`C = (q)/(V) = (q^(2))/(W)`
`[X] rarr [C] = [M^(-1)L^(-2)T^(2)Q^(2)`
And `[B] = ([F)/(iL])`
`[Z] rarr [B] = [(MLT^(-2))/(QT^(-1)L)]= [MT^(-1)Q^(-1)]`
given `Y = (X)/(3Z^(2))`
`[T] =[(M^(-1)L^(-2)T^(2)Q^(2)])/(MT^(-1)Q^(-1))]^(2) = [M^(-3)L^(-2)T^(-4)Q^(4)]`.