Question

Out of the following physical quantities which quantity has the same unit as that of Planck's constant?

• A. moment of force
• B. power
• C. angular momentum
• D. moment of inertia

Hint:

Whenever you see Planck's constant, think of \textbf{Bohr's Second Postulate}. It explicitly links the "action" of an electron to an integer multiple of $h/2\pi$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Planck's constant ($h$) appears in the equation $E = h\nu$. We can determine its units by analyzing its dimensions.
Step 2: Detailed Explanation:
The unit of Planck's constant is Joule-second (J$\cdot$s).

• Angular Momentum ($L$): $L = mvr$. Units are $\text{kg}\cdot\text{m}^2/\text{s}$, which is equivalent to $\text{J}\cdot\text{s}$.
• Moment of force (Torque): $\text{N}\cdot\text{m}$ (or Joule).
• Power: $\text{J/s}$ (Watt).

According to Bohr's quantization rule, $L = \frac{nh}{2\pi}$, which directly shows that $L$ and $h$ must have the same units.
Step 3: Final Answer:
The correct option is (c).