The provided reference discusses the SI unit of 'g', which is the acceleration due to gravity (measured in m/s²). However, the question asks for the SI unit of 'G', which is the universal gravitational constant. These are two distinct physical quantities. Therefore, the direct answer from the provided reference is not applicable.
The SI unit for the universal gravitational constant (G) is N⋅m²/kg².
Here's a breakdown of why:
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G's role: The gravitational constant (G) is a fundamental physical constant that appears in Newton's law of universal gravitation. This law states that the gravitational force (F) between two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) between their centers. Mathematically, this is expressed as:
F = G (m1 m2) / r²
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Isolating G: To find the unit of G, we rearrange the formula to solve for G:
G = F r² / (m1 m2)
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Analyzing Units:
- Force (F) is measured in Newtons (N).
- Distance (r) is measured in meters (m).
- Mass (m1 and m2) is measured in kilograms (kg).
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Combining Units: By substituting the SI units into the formula for G, we get:
G = (N m²) / (kg kg) = N⋅m²/kg²
Therefore, the SI unit of the universal gravitational constant (G) is N⋅m²/kg².
