In physics, the capital letter 'G' stands for the Universal Gravitational Constant. This is a massive, unchanging number that dictates the strength of gravity across the entire universe, pulling planets and stars together.
The dimensional formula of the Universal Gravitational Constant (G) is [Mā»Ā¹ LĀ³ Tā»Ā²].
Quantity: Universal Gravitational Constant (Capital 'G').
Formula Used: Newton's Law of Gravitation [F = G(m1m2)/rĀ²].
Dimensional Formula: [Mā»Ā¹ LĀ³ Tā»Ā²].
SI Unit: NĀ·mĀ²/kgĀ².
Universal Value: The value of G is exactly 6.674 Ć 10ā»Ā¹Ā¹ NĀ·mĀ²/kgĀ² everywhere in the universe.
We cannot guess the dimension of G. We must derive it mathematically using Newton's Universal Law of Gravitation. The formula states the force (F) between two masses (m1 and m2) separated by a distance (r) is:
F = G (m1 Ć m2) / rĀ²
Step 1: Rearrange the formula to isolate 'G' on one side: G = (F Ć rĀ²) / (m1 Ć m2)
Step 2: Substitute the known dimensions of Force, Distance, and Mass into the equation.
Step 3: Put them into the rearranged formula: G = ( [MĀ¹ LĀ¹ Tā»Ā²] Ć [LĀ²] ) / [MĀ²]
Step 4: Simplify the equation using basic algebra (laws of exponents):
Final Dimension of G = [Mā»Ā¹ LĀ³ Tā»Ā²].
Using the formula G = (F Ć rĀ²) / (m1 Ć m2), we can also find the SI unit without memorizing it:
The dimensional formula for capital G is [Mā»Ā¹ LĀ³ Tā»Ā²].
You rearrange Newton's Law of Gravitation to G = (F Ć rĀ²) / (m1 Ć m2). Then, you plug in the dimensions for force [MLTā»Ā²], distance [LĀ²], and mass [MĀ²] and simplify.
No. Capital G is a universal constant with dimension [Mā»Ā¹ LĀ³ Tā»Ā²]. Small g is acceleration due to gravity with dimension [Mā° LĀ¹ Tā»Ā²].
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