Dimensions Of Hubble's constant are

The correct option is [T⁻¹].

Let us derive the dimensions of Hubble's constant step-by-step.

According to Hubble's law, the recessional velocity ($v$) of a galaxy is directly proportional to its distance ($d$) from the observer. Mathematically, this is expressed as:
$v=H_{0}d$
where $H_0$ is Hubble's constant.

We can rearrange the formula to solve for Hubble's constant:
$H_0=\frac{v}{d}$

Now, let us find the dimensional formula of each quantity:
1. Velocity ($v$) represents displacement per unit time. Its dimensional formula is:
$\left[v\right]=\left[L{T}^{-1}\right]$
2. Distance ($d$) represents length. Its dimensional formula is:
$\left[d\right]=\left[L\right]$

Substituting these dimensions into the expression for Hubble's constant, we get:
$\left[H_0\right]=\frac{\left[L{T}^{-1}\right]}{\left[L\right]}$
$\left[H_0\right]=\left[T^{-1}\right]$

Therefore, the dimensions of Hubble's constant are [T⁻¹] (or $\left[M^0{L}^0{T}^{-1}\right]$).