Question

The dimensions of Hubble constant is:
A. \[\left[ {{T}^{-1}} \right]\]
B. $\left[ {{M}^{0}}{{L}^{0}}{{T}^{-2}} \right]$
C. $\left[ ML{{T}^{4}} \right]$
D. $\left[ M{{T}^{-1}} \right]$

Answer 1

Hint: Hubble’s constant is a constant used in cosmology which shows how fast a galaxy recedes from us per second due to expansion of the universe. Simply speaking, it is a proportionality that relates to the velocity and displacement of the galaxies. Notice the term per second in the definition, it will give you an idea about the dimension of Hubble’s constant.

Complete Step-by-Step solution:
Hubble’s Constant is the byproduct of Hubble’s Law in physical cosmology which states that- ‘The galaxies are receding away from us at a velocity which is proportional to the distance from us’. Here the term ‘us’ means earth. So if the galaxy is very far away from us, the velocity of recession will also be faster.
We can write Hubble’s Law as simple equation as follows,
$\text{Velocity of the galaxy}=\text{Hubble Constant}\times \left( \text{Distance of the galaxy from earth} \right)$
So we know that the dimensional formula for the velocity is $\left[ L{{T}^{-1}} \right]$ and the dimensional formula for distance is $\left[ L \right]$. So the dimension formula for the Hubble’s constant can be written as,
$\text{Hubble }\!\!'\!\!\text{ s Constant}=\dfrac{\left[ \text{Velocity} \right]}{\left[ \text{Distance} \right]}=\dfrac{\left[ L{{T}^{-1}} \right]}{\left[ L \right]}$
$\therefore \text{Hubble }\!\!'\!\!\text{ s Constant}=\left[ {{T}^{-1}} \right]$
So the dimensional formula of the Hubble’s constant is found to be $\left[ {{T}^{-1}} \right]$.
So the answer to the question is option (A)- $\left[ {{T}^{-1}} \right]$.

Additional Information:
Edwin Hubble postulated his famous law in the 1920s which came to be later known as the Hubble’s law, which showed that the galaxies which are not in the milky way cluster receded away from with a velocity proportional to the distance away from the earth.
The value of Hubble’s constant has changed over the years because of better measurement techniques in determining the Redshift produced by the galaxies.

Note: The dimensional formula of the Hubble’s constant is the same as that of frequency and angular frequency.
The value of Hubble’s Constant has changed over the years. Initially it was $150\text{ }\dfrac{km}{\left( s\times Mpc \right)}$, where s is in seconds, pc stands for parsec which is a unit for distance in astronomy and cosmology.
The current value of Hubble's constant is approximately $\text{69 }\dfrac{km}{\left( s\times Mpc \right)}$.