Question

Choose the correct answer from the options given below:

LIST I		LIST II
A	Planck's constant (h)	1	\(\left[ M ^1 L ^2 T ^{-2}\right]\)
B	Stopping potential (Vs)	2	\(\left[ M ^1 L ^1 T ^{-1}\right]\)
C	Work function (ø)	3	\(\left[ M ^1 L ^2 T ^{-1}\right]\)
D	Momentum (p)	4	\(\left[ M ^1 L ^2 T ^{-3} A ^{-1}\right]\)

• A. A-II, B-IV, C-III, D-I
• B. A-III, B-IV, C-I, D-II
• C. A-I, B-III, C-IV, D-II
• D. A-III, B-I, C-II, D-IV

Answer 1

The Correct Option is B

(A) Planck's constant (\(h\)): Energy is given by \(E = h \nu\). Using the dimensional formula of energy: \[ [E] = M^1 L^2 T^{-2}, \quad [\nu] = T^{-1} \] Thus: \[ [h] = \frac{[E]}{[\nu]} = \frac{M^1 L^2 T^{-2}}{T^{-1}} = M^1 L^2 T^{-1} \] Match: \(A \rightarrow \text{III}\). (B) Stopping potential (\(V_s\)): Voltage is given by \(V = \frac{E}{q}\). Using dimensional formulas: \[ [V] = \frac{M^1 L^2 T^{-2}}{A T^{-1}} = M^1 L^2 T^{-3} A^{-1} \] Match: \(B \rightarrow \text{IV}\). (C) Work function (\(\phi\)): Work function is a form of energy: \[ [\phi] = M^1 L^2 T^{-2} \] Match: \(C \rightarrow \text{I}\). (D) Momentum (\(p\)): Momentum is given by \(p = F \cdot t\). Using dimensional formulas: \[ [p] = M^1 L^1 T^{-2} \cdot T^1 = M^1 L^1 T^{-1} \] Match: \(D \rightarrow \text{II}\). Thus, the correct matching is \(A \rightarrow \text{III}, B \rightarrow \text{IV}, C \rightarrow \text{I}, D \rightarrow \text{II}\).