Question

Match List - I with List - II :
List - I: (a) h (Planck's constant), (b) E (kinetic energy), (c) V (electric potential), (d) P (linear momentum)
List - II: (i) [M L T$^{-1}$], (ii) [M L$^2$ T$^{-1}$], (iii) [M L$^2$ T$^{-2}$], (iv) [M L$^2$ T$^{-3}$ I$^{-1}$]
Choose the correct answer from the options given below :

• (a) → (i), (b) → (ii), (c) → (iv), (d) → (iii)
• (a) → (iii), (b) → (iv), (c) → (ii), (d) → (i)
• (a) → (ii), (b) → (iii), (c) → (iv), (d) → (i)
• (a) → (iii), (b) → (ii), (c) → (iv), (d) → (i)

Hint:

Planck's constant ($h$) has the same dimensions as angular momentum ($L = mvr$). Linear momentum is mass $\times$ velocity, while energy is always $[ML^2T^{-2}]$.

Answer 1

The Correct Option is C

Step 1: Planck's constant $h = E/f$. Units: $\text{J} \cdot \text{s}$. Dimensions: $[ML^2T^{-2}][T] = [ML^2T^{-1}]$. Match: (ii).
Step 2: Kinetic Energy $E$. Dimensions: $[ML^2T^{-2}]$. Match: (iii).
Step 3: Electric Potential $V = \text{Work}/\text{Charge}$. Dimensions: $[ML^2T^{-2}] / [IT] = [ML^2T^{-3}I^{-1}]$. Match: (iv).
Step 4: Linear Momentum $P = mv$. Dimensions: $[M][LT^{-1}] = [MLT^{-1}]$. Match: (i).