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
$=\frac{V\times Q}{\text{Volume}}=\frac{\text{Vlt}}{\text{Volume}}=\frac{\text{Power}\times \text{Time}}{\text{Volume}}$
$\Rightarrow \frac{\left[M{L}^2{T}^{-3}\right]\left[T\right]}{\left[L^3\right]}=\left[M{L}^{-1}{T}^{-2}\right]$
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.