Question

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

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

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
To solve this matching question, we need to determine the dimensional formula for each physical quantity listed in List-I using standard physics equations relating them to basic mechanical and electrical dimensions.

Step 2: Key Formula or Approach:
Energy $E = [M L^2 T^{-2}]$
Planck's constant $h$: $E = h\nu$
Stopping potential $V$: $E = qV$ where $q = I \cdot t = [A T]$
Work function $\Phi$: A form of Energy.
Threshold frequency $\nu_0$: Frequency.

Step 3: Detailed Explanation:
1. Planck's Constant (A):
From $E = h\nu \implies h = \frac{E}{\nu}$.
Dimension of $E = [M L^2 T^{-2}]$. Dimension of $\nu = [T^{-1}]$.
$[h] = \frac{[M L^2 T^{-2}]}{[T^{-1}]} = [M L^2 T^{-1}]$.
So, A matches with III.
2. Stopping Potential (B):
From Work done/Energy $E = qV \implies V = \frac{E}{q}$.
Dimension of charge $q = [A T]$.
$[V] = \frac{[M L^2 T^{-2}]}{[A T]} = [M L^2 T^{-3} A^{-1}]$.
So, B matches with IV.
3. Work Function (C):
Work function is the minimum energy required to remove an electron. It has the exact same dimensions as Energy.
$[\Phi] = [M L^2 T^{-2}]$.
So, C matches with I.
4. Threshold frequency (D):
Frequency is the inverse of time period.
$[\nu_0] = [T^{-1}]$.
So, D matches with II.
The correct sequence is A-III, B-IV, C-I, D-II.

Step 4: Final Answer:
Option (A) is correct.