Match List I with List II.
$$\begin{array}{|l|l|l|l|}\hline & \text{List I (Physical quantity)} & & \text{List II (Dimensional formula)} \\ \hline \text{A.} & \text{Pressure gradient} & \text{I.} & [\text{M}^0\text{L}^2\text{T}^{-2}] \\ \hline \text{B.} & \text{Energy density} & \text{II.} & [\text{M}^1\text{L}^{-1}\text{T}^{-2}] \\ \hline \text{C.} & \text{Electric field} & \text{III.} & [\text{M}^1\text{L}^{-2}\text{T}^{-2}] \\ \hline \text{D.} & \text{Latent heat} & \text{IV.} & [\text{M}^1\text{L}^1\text{T}^{-3}\text{A}^{-1}] \\ \hline \end{array}$$
Choose the correct answer from the options given below:
Answer: (C) A-III, B-II, C-IV, D-I
- Pressure gradient $=\dfrac{\text{pressure}}{\text{length}}$: $[\text{M}\text{L}^{-1}\text{T}^{-2}]/[\text{L}] = [\text{M}\text{L}^{-2}\text{T}^{-2}]$ → III
- Energy density $=\dfrac{\text{energy}}{\text{volume}}$: $[\text{M}\text{L}^{2}\text{T}^{-2}]/[\text{L}^3] = [\text{M}\text{L}^{-1}\text{T}^{-2}]$ → II
- Electric field $=\dfrac{F}{q}$: $[\text{M}\text{L}\text{T}^{-2}]/[\text{A}\text{T}] = [\text{M}\text{L}\text{T}^{-3}\text{A}^{-1}]$ → IV
- Latent heat $=\dfrac{Q}{m}$: $[\text{M}^0\text{L}^2\text{T}^{-2}]$ → I
So A-III, B-II, C-IV, D-I.
Solution by Sreeraj P, M.Sc Physics