Question

What is the dimension of the Gravitational constant?

Answer 1

Derivation:
The formula for gravitational force is given by 2 F =G ⋅ r 2 m 1​⋅ m 2​​.
Alternatively, we can express G using dimensional analysis:
Starting with 2 F =G ⋅ r 2 m 1​⋅ m 2​​, we rearrange it to solve for G :
2 G =m 1​⋅ m 2​ F ⋅ r 2​ . . . . . (1)
Here, G represents the Universal Gravitational Constant.
Now, let's analyze the dimensions of the involved quantities:
Mass has dimensions: [M] Radius has dimensions: [L] Force has dimensions: [M ⋅ L ⋅ T −2]
Substituting these dimensions into equation (1), we get:
G =[M]⋅[M][M ⋅ L ⋅ T −2]⋅[L]2​
Simplifying further:
G =[M −1⋅ L 3⋅ T −2]
Hence, the dimension of the Universal Gravitational Constant (G) is [M −1⋅ L 3⋅ T −2].
M-1L3T-2