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In the formula $X = 3 Y Z^{2}$ , $X$ and $Z$ have dimensions of capacitance and magnetic induction respectively. What are the dimensions of $Y$ in $M K S Q$ system?

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$[M^{- 3} L^{- 1} T^{3} Q^{4}]$

$[M^{- 3} L^{- 2} T^{4} Q^{4}]$

$[M^{- 2} L^{- 2} T^{4} Q^{4}]$

$[M^{- 3} L^{- 2} T^{4} Q]$

answer is B.

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Detailed Solution

$[Y] = [\frac{X}{z^{2}}] = [\frac{Capacitance}{(Magnetic induction)^{2}}]$

$= [\frac{M^{- 1} L^{- 2} Q^{2} T^{2}}{M^{2} Q^{- 2} T^{- 2}}]$

$= [M^{- 3} L^{- 2} T^{4} Q^{4}]$

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