Question: The dimensions of Planck’s constant equals to that of: [PMT/NEET-2001]
a. energy
b. momentum
c. angular momentum
d. power

Answer: (c) angular momentum. Planck’s constant has the dimensions of action, the same as angular momentum.

Solution:

From $E = h\nu$:

$ [h] = [E]/[\nu] = (ML^{2}T^{-2})/(T^{-1}) = ML^{2}T^{-1} $.

Angular momentum $L = r \times p$:

$ [L] = [r][p] = L \cdot (MLT^{-1}) = ML^{2}T^{-1} $.

In SI units, $h$ is in joule-second (J·s), i.e., $ \text{kg}\,\text{m}^{2}\,\text{s}^{-1} $, matching angular momentum.

Option check:

Power: $ML^{2}T^{-3}$ → not equal

Energy: $ML^{2}T^{-2}$ → not equal

Momentum: $MLT^{-1}$ → not equal

Angular momentum: $ML^{2}T^{-1}$ → equal