First slide

Dimensions of physical quantities

Question

Of the following quantities, which one has the dimensions different from the remaining three?

Moderate

A

Energy density
B

Force per unit area
C

Product of charge per unit volume and voltage
D

Angular momentum per unit mass

Solution

$\begin{array}{l} Energy density = \frac{Energy}{Volume} = [{ML}^{- 1} T^{- 2}] \\ Force/Area = {ML}^{- 1} T^{- 2} [Charge / Volume] \times [Voltage] \\ = \frac{Q}{Volume} \times \frac{W}{Q} = \frac{Work}{Volume} = {ML}^{- 1} T^{- 2} \end{array}$

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