First slide

Dimensions of physical quantities

Question

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?

Moderate

A

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

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

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

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

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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