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

Options

A. `[M^(-3)L^(-2)T^(-2)Q^(-4)]`
B. `[ML^(-2)]`
C. `[M^(-3)L^(-2)Q^(4)T^(8)]`
D. `[M^(-3)L^(-2)Q^(4)T^(4)]`

Answer

D

Explanation

[Capacitance A] `[M^(-1) L 6 - 2 T^(2) Q^(2)]`
[Magnetic induction C] `= [MT^(-1) Q^(-1)]`
`[C]^(2) =[M^(2) T^(-2) Q^(-2)]`
Given , A = `3BC^(2) or B = (A)/(3C^(2)) rArr [B] ([A])/([C]^(2))`
`therefore [B] = ([M^(-1)L^(-2)T^(2)Q^(2)])/([M^(2)T^(-1)Q^(-2)])=[M^(-3)L^(-2)T^(4)Q^(4)]`