Question

Match the given quantities according to their dimensions: 


 

• A. A-R, B-S, C-Q, D-P
• B. A-S, B-R, C-P, D-Q
• C. A-S, B-R, C-Q, D-P
• D. A-P, B-Q, C-R, D-S

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Dimensional analysis involves expressing physical quantities in terms of fundamental dimensions: Mass (M), Length (L), Time (T), and Current (A).
Step 2: Key Formula or Approach:
1. Work Function (\( \phi \)) is energy: \( [ML^2T^{-2}] \). 2. Planck's constant (\( h \)): \( E = hf \implies h = E/f \). 3. Potential (\( V \)): \( V = W/q \). 4. Frequency (\( f \)): \( 1/T \).
Step 3: Detailed Explanation:
- (A) Work Function: It is energy required to eject an electron. Energy = Force \(\times\) Distance = \( [MLT^{-2} \cdot L] = [ML^2T^{-2}] \). Matches (S). - (B) Planck's constant: \( [h] = \frac{[Energy]}{[f]} = \frac{ML^2T^{-2}}{T^{-1}} = [ML^2T^{-1}] \). Matches (R). - (C) Stopping Potential: \( [V] = \frac{[Work]}{[Charge]} = \frac{ML^2T^{-2}}{AT} = [ML^2T^{-3}A^{-1}] \). Matches (Q). - (D) Frequency: \( [f] = [T^{-1}] \). Matches (P).
Step 4: Final Answer:
The correct matching is A-S, B-R, C-Q, D-P.