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 MKSQ system?

Moderate

A

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

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

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

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

Solution

$\begin{array}{l} C = \frac{q}{V} = \frac{q^{2}}{W} \\ [X] \to [C] = [M^{- 1} L^{- 2} T^{2} Q^{2}] \\ And [B] = [\frac{F}{i L}] \\ [Z] \to [B] = [\frac{M L T^{- 2}}{Q T^{- 1} L}] = [M T^{- 1} Q^{- 1}] \end{array}$
$\begin{array}{l} Given, Y = \frac{X}{3 Z^{2}} \\ [Y] = \frac{[M^{- 1} L^{- 2} T^{2} Q^{2}]}{{[M T^{- 1} Q^{- 1}]}^{2}} = [M^{- 3} L^{- 2} T^{4} Q^{4}] \end{array}$

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