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In the equation $X = 3 Y Z^{2}, X a n d Z$ have dimensions of capacitance and magnetic induction respectively. In MKSQ system, the dimensional formula of Y is

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

$[M L^{- 2}]$

$[M^{- 3} L^{- 2} Q^{4} T^{8}]$

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

answer is D.

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Detailed Solution

Capacitance $X = [M^{- 1} L^{- 2} T^{2} Q^{2}]$

Magnetic induction $Z = [M T^{- 1} Q^{- 1}]$

${[Z]}^{2} = [M^{2} T^{- 2} Q^{- 2}]$

Given, $X = 3 Y Z^{2}$

or $Y = \frac{X}{3 Z^{2}} o r [Y] = \frac{[X]}{{[Z]}^{2}}$

$∴ [Y] = \frac{[M^{- 1} L^{- 2} T^{2} Q^{2}]}{[M^{2} T^{- 2} Q^{- 2}]} = [M^{- 3} L^{- 2} T^{4} Q^{4}]$

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