JEE Physics 2023 Question with Solution

Given: Match physical quantities with their dimensional formulae.

Find: The correct correspondence between List I and List II.

Use the dimensional formula of each quantity:

• Planck's constant $h$ has dimensions of energy $\times$ time.

$$[h] = [ML^2T^{-2}] [T] = ML^2T^{-1}$$

So, A \rightarrow III.

• Stopping potential $V_s$ has the dimensions of electric potential.

$$[V_s] = \frac{\text{work}}{\text{charge}} = \frac{ML^2T^{-2}}{AT} = ML^2T^{-3}A^{-1}$$

So, B \rightarrow IV.

• Work function $\Phi$ is an energy.

$$[\Phi] = ML^2T^{-2}$$

So, C \rightarrow I.

• Momentum $p$ is mass $\times$ velocity.

$$[p] = M \times LT^{-1} = MLT^{-1}$$

So, D \rightarrow II.

Therefore, the correct matching is A-III, B-IV, C-I, D-II. Hence, the correct option is B.

Note: The solution appears unrelated to this question and discusses frequency ranges of communication systems. The answer has therefore been resolved from the dimensional analysis of the given question and the listed options.