Planck's constant has the same dimensions as those of

The correct answer is Option (4) → force x distance x time

From Planck’s relation \( E = h\nu \), Planck’s constant is energy divided by frequency, that is energy multiplied by time.

    \( \displaystyle h = \frac{E}{\nu} \;\Rightarrow\; [h] = [\mathrm{ML^{2}T^{-2}}][\mathrm{T}] = [\mathrm{ML^{2}T^{-1}}] \)

Since energy = force × distance, compare each option:

Option (1) force x distance — Incorrect. Force × distance is work or energy, \( [\mathrm{ML^{2}T^{-2}}] \).

Option (2) force x speed — Incorrect. Force × speed is power, \( [\mathrm{ML^{2}T^{-3}}] \).

Option (3) force x time — Incorrect. Force × time is impulse (change in momentum), \( [\mathrm{MLT^{-1}}] \).

Option (4) force x distance x time — Correct. Force × distance × time is energy × time, \( [\mathrm{ML^{2}T^{-1}}] \), the same as h.