Physics

# 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 ________.

$-3$ in mass, $-2$ in length, $4$ in time and $4$ in charge.

##### SOLUTION
Given,

$X=3YZ^2$

Then,

$Y=\dfrac{X}{3Z^2}$

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

$[Z]=[B]=[MT^{-1}Q^{-1}]$

Then,

$[Y]=\dfrac{[X]}{[3Z^2]}$

$=\dfrac{[M^{-1}L^{-2}T^2Q^2]}{[MT^{-1}Q^{-1}]^2}=[M^{-3}L^{-2}T^4Q^4]$

That is,

$-3$ in mass, $-2$ in length, $4$ in time and $4$ in charge.

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Single Correct Medium Published on 18th 08, 2020
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