Question

The dimensions of intensity are,

• A. $M{L}^0{T}^{-3}$
• B. $M^2{L}^1{T}^{-2}$
• C. $M{L}^2{T}^{-2}$
• D. $M^2{L}^2{T}^{-3}$

Answer 1

The correct option is A

$M{L}^0{T}^{-3}$

The wave's intensity is defined as the energy transferred per unit area per unit of time.

$I=\frac{E}{At}$

Now substituting the dimensions of energy$\left[M{L}^2{T}^{-2}\right]$, time$\left[T\right]$ and area$\left[L^2\right]$, we get

$$\begin{gathered} I=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[L^2\right]\left[T\right]} \\ I=\left[M{L}^0{T}^{-3}\right] \end{gathered}$$

Therefore the dimensional formula of the intensity $M{L}^0{T}^{-3}$.

Hence, the correct option is A.