The dimensions of Planck's constant are

The correct option is [ML²T⁻¹].

To find the dimensions of Planck's constant, we can use Planck's equation, which relates the energy of a photon to its frequency:

$E=hf$

Where:
- $E$ represents Energy
- $h$ represents Planck's constant
- $f$ represents frequency

Rearranging the equation to solve for Planck's constant ($h$):

$h=\frac{E}{f}$

Let's determine the dimensions of each quantity step-by-step:

1. Dimensions of Energy ($E$):
Energy has the same dimensions as work done. Work is defined as Force multiplied by displacement.
Work = Force × displacement
Since Force = mass × acceleration, its dimensions are:
Force = [M] × [LT^-2] = [MLT^-2]
Therefore, the dimensional formula of Energy is:
Energy = Force × displacement = [MLT^-2] × [L] = [ML²T^-2]

2. Dimensions of Frequency ($f$):
Frequency is the reciprocal of the time period ($f=\frac{1}{T}$).
Therefore, its dimensional formula is:
Frequency = [T^-1]

3. Dimensions of Planck's Constant ($h$):
Now, substitute the dimensional formulas of Energy and frequency into the rearranged equation:

$\left[h\right]=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[T^{-1}\right]}$

Simplifying the powers of Time (T):

$\left[h\right]=\left[M{L}^2{T}^{-2-(-1)}\right]=\left[M{L}^2{T}^{-1}\right]$

Thus, the dimensional formula of Planck's constant is [ML²T⁻¹].