What is the Dimensional Formula of 'g' (Acceleration Due to Gravity)?

Even though gravity is a mysterious force, small 'g' is simply a type of Acceleration. Therefore, its dimensional formula is exactly identical to the standard formula for acceleration.

Let's break it down:

1. The basic formula for acceleration is: Change in Velocity / Time taken.
2. Velocity is: Distance / Time.
3. Putting it together: Acceleration = Distance / (Time × Time).

Now, let's assign the fundamental dimensions:

• Distance = Length [L].
• Time = [T].
• Therefore: [L] / [T²]
• Moving T to the numerator: [L¹ T⁻²].

To write it in the standard [M L T] format, we must include Mass. Since the acceleration of a falling object does NOT depend on its mass (a feather and a bowling ball fall at the same speed in a vacuum), the Mass dimension is zero.

Final Dimensional Formula: [M⁰ L¹ T⁻²].

Looking at the dimension [L¹ T⁻²], we can easily derive the official SI unit for small 'g'.

• [L] = meters (m)
• [T⁻²] = per second squared (/s²) Therefore, the SI unit of 'g' is m/s². (On the surface of the Earth, its value is 9.8 m/s²).