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 per unit mass

Answer 1

The correct option is D Angular momentum per unit mass

Energy per unit volume
$=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[L^3\right]}=\left[M{L}^{-1}{T}^{-2}\right]$

Force per unit area
$=\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]}=\left[M{L}^{-1}{T}^{-2}\right]$

Product of voltage and charge per unit volume
$=\frac{V\times Q}{Volume}=\frac{Vlt}{Volume}$
$=\frac{Power\times Time}{Volume}$
$\Rightarrow \frac{\left[M{L}^2{T}^{-3}\right]\left[T\right]}{\left[L^3\right]}=\left[M{L}^{-1}{T}^{-2}\right]$

Angular momentum per unit mass:
$=\frac{\left[M{L}^2{T}^{-1}\right]}{\left[M\right]}=\left[L^2{T}^{-1}\right]$

So angular momentum per unit mass has different dimension.