Question

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

• A. Energy per unit volume
• B. Force per unit area
• C. Product of voltage and charge per unit volume
• D. Angular momentum

Answer 1

Answer: (D)

Angular momentum

Answer 2

Dimensions of energy $E=[ML^2 T^{-2}]$ Dimensions of volume $v=[L^3]$ Dimensions of force $F=[MLT^{-2}]$ Dimensions of area $A=[L^2]$ Dimensions of voltage $V=[ML^2T^{-3}A^{-1}]$ Dimensions of charge $q=[AT]$ Dimensions of angular momentum $L=[ML^2T^{-1}]$ $\therefore$ Dimensions of $\frac{E}{v}=\frac{[ML^2T^{-2}]}{[L^3]}=[ML^{-1}T^{-2}]$ Dimensions of $\frac{F}{A}=\frac{[MLT^{-2}]}{[L^2]}=[ML^{-1}T^{-2}]$ Dimensions of $\frac{V_q}{v}=\frac{[ML^2T^{-3}A^{-1}][AT]}{[L^3]}=[ML^{-1}T^{-2}]$ Dimensions of angular momentum is $[ML^2T^{-1}]$ while other three has dimensions $[ML^{-1}T^{-2}]$