In physics, there is a massive difference between the small letter 'g' and the capital letter 'G'. While 'G' is the Universal Gravitational Constant, the small 'g' stands for the Acceleration Due to Gravity (the rate at which an object speeds up as it falls towards the Earth).
The dimensional formula of 'g' is [M⁰ L¹ T⁻²].
Quantity: Acceleration due to Gravity (small 'g').
Dimensional Formula: [M⁰ L¹ T⁻²].
SI Unit: meters per second squared (m/s²).
Value on Earth: Approximately 9.8 m/s².
Crucial Rule: Small 'g' is an acceleration, it is NOT a Force. (Force of gravity is Weight = mg).
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:
Now, let's assign the fundamental dimensions:
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'.
The dimensional formula for acceleration due to gravity (g) is [M⁰ L¹ T⁻²].
Because the acceleration of a falling object is completely independent of its mass. Therefore, the mass dimension [M] is raised to the power of zero.
Yes, they are completely different. Small 'g' is an acceleration [L T⁻²], while capital 'G' is the Universal Gravitational Constant [M⁻¹ L³ T⁻²].
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