Question

List-I presents some physical quantities and List-II presents their dimensions. Match the two lists appropriately. 

• A. A\(\rightarrow\)(3); B\(\rightarrow\)(4); C\(\rightarrow\)(2); D\(\rightarrow\)(1)
• B. A\(\rightarrow\)(3); B\(\rightarrow\)(1); C\(\rightarrow\)(4); D\(\rightarrow\)(2)
• C. A\(\rightarrow\)(2); B\(\rightarrow\)(3); C\(\rightarrow\)(4); D\(\rightarrow\)(1)
• D. A\(\rightarrow\)(4); B\(\rightarrow\)(3); C\(\rightarrow\)(1); D\(\rightarrow\)(2)

Answer 1

The Correct Option is B

Concept: Use basic dimensional formulas of common physical quantities.

• Energy (or work) \(= ML^2T^{-2}\)
• Potential \(= \dfrac{\text{Energy}}{\text{Charge}}\)
• Frequency \(= T^{-1}\)
• Planck's constant \(h = \dfrac{\text{Energy}}{\text{frequency}}\)

Step 1: Work function \(\phi\). Work function is energy. \[ [\phi] = ML^2T^{-2} \] \[ A \rightarrow (3) \] Step 2: Stopping potential \(V_s\). \[ V = \frac{\text{Energy}}{\text{Charge}} \] Charge dimension \(= IT\) \[ [V] = \frac{ML^2T^{-2}}{IT} \] \[ [V] = ML^2T^{-3}I^{-1} \] \[ B \rightarrow (1) \] Step 3: Planck's constant \(h\). \[ h = \frac{\text{Energy}}{\text{frequency}} \] \[ [h] = \frac{ML^2T^{-2}}{T^{-1}} \] \[ [h] = ML^2T^{-1} \] \[ C \rightarrow (4) \] Step 4: Frequency \(f\). \[ [f] = T^{-1} \] \[ D \rightarrow (2) \] Thus, \[ A \rightarrow (3), \quad B \rightarrow (1), \quad C \rightarrow (4), \quad D \rightarrow (2) \]