The dimension of Planck's constant is

The correct option is [ML²T⁻¹].

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

$E=h\nu$

Where:
- $E$ is the energy of the photon
- $h$ is Planck's constant
- $\nu$ is the frequency of the photon

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

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

Now, we determine the dimensional formulas for energy ($E$) and frequency ($\nu$):

1. Energy ($E$): Energy has the same dimensions as work done (Force × Displacement). Since Force = Mass × Acceleration:

$\left[\text{Force}\right]=\left[{\text{MLT}}^{-2}\right]$

$\left[\text{Energy}\right]=\left[\text{Force}\right]\times \left[\text{Displacement}\right]=\left[{\text{MLT}}^{-2}\right]\times \left[\text{L}\right]=\left[{\text{ML}}^2{\text{T}}^{-2}\right]$

2. Frequency ($\nu$): Frequency is defined as the reciprocal of the time period:

$\left[\nu \right]=\left[{\text{T}}^{-1}\right]$

Substituting these dimensional formulas back into the rearranged equation for Planck's constant:

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

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

$\left[h\right]=\left[{\text{ML}}^2{\text{T}}^{-1}\right]$

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