Question: Of the following quantities, which one has dimensions different from the remaining three? [PMT/NEET-1989]
a. Energy per unit volume
b. Force per unit area
c. Product of voltage and charge per unit volume
d. Angular momentum

Solution

• Energy per unit volume: $\dfrac{ML^{2}T^{-2}}{L^{3}} = ML^{-1}T^{-2}$
• Force per unit area (Pressure): $\dfrac{MLT^{-2}}{L^{2}} = ML^{-1}T^{-2}$
• Product of voltage and charge per unit volume:
  Voltage × charge = Energy, so $\dfrac{ML^{2}T^{-2}}{L^{3}} = ML^{-1}T^{-2}$
• Angular momentum: $ML^{2}T^{-1}$

All first three are same, but angular momentum is different.

Answer
d. Angular momentum