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In the formula $X = 5 Y Z^{2}, X a n d Z$ have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?

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

$[M^{- 1} L^{- 2} T^{4} A^{2}]$

$[M^{- 1} L^{0} T^{- 4} A^{- 2}]$

$[M^{- 2} L^{- 2} T^{6} A^{3}]$

answer is A.

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Detailed Solution

$X = 5 Y Z^{2} \Rightarrow Y α \frac{X}{Z^{2}} ......... (i)$

$X =$ capacitance $= \frac{Q}{V} = \frac{Q^{2}}{W} = \frac{[A^{2} T^{2}]}{[M L^{2} T^{- 2}]}$

$X = [M^{- 1} L^{- 2} T^{4} A^{2}], Z = B = \frac{F}{I L}, Z = [M T^{- 2} A^{- 1}]$

$Y = \frac{[M^{- 1} L^{- 2} T^{4} A^{2}]}{{[M T^{- 2} A^{- 1}]}^{2}}, Y = [M^{- 3} L^{- 2} T^{8} A^{4}]$

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