Small ' g ' is acceleration due to gravity.
Acceleration = Rate of change of velocity.
In units,
Acceleration = ( m/s)/s = m/s^-2
Dimensions of acceleration = [ LT^-2]
Therefore, Dimensional Formula of Small g ( acceleration due to gravity) is [ LT^-2].

The Dimensional Formula of Small g

Small g is the acceleration due to gravity, which is defined as the force that attracts two objects towards each other. It is usually denoted by 'g' and is expressed in units of meters per second squared (m/s^2). The dimensional formula for small g can be determined using the principle of dimensional analysis.

Principle of Dimensional Analysis

The principle of dimensional analysis states that any physical quantity can be expressed as a product of its fundamental units, where the fundamental units are mass (kg), length (m), and time (s). The dimensional formula for any physical quantity can be obtained by equating the dimensions of the fundamental units in the expression for that quantity.

Dimensional Formula of Small g

The dimensional formula for small g can be obtained by using the formula for acceleration, which is given as:

Acceleration (a) = Force (F) / Mass (m)

The dimensional formula for force is given as:

Force (F) = Mass (m) x Acceleration (a)

Therefore, we can express the dimensional formula for small g as:

Small g = Force (F) / Mass (m) = Mass (m) x Acceleration (a) / Mass (m) = Acceleration (a)

Hence, the dimensional formula for small g is [T^-2], where T represents time.

Conclusion

To summarize, the dimensional formula for small g is [T^-2], which means it has the dimensions of inverse square of time. This implies that small g is a measure of the rate at which the velocity of an object changes with respect to time due to the gravitational attraction between two objects.