What is the SI unit of the gravitational constant G?

The gravitational constant, denoted as G, is a fundamental physical constant that appears in Newton's law of universal gravitation and Einstein's theory of general relativity. It quantifies the strength of the gravitational force between two masses. The SI unit of G is indeed Nm²/kg², which is derived from the formula that describes the gravitational force, F = G(m₁m₂)/r². In this formula, F is the gravitational force measured in Newtons, m₁ and m₂ are the masses measured in kilograms, and r is the distance between the centers of the two masses measured in meters.

The unit Nm²/kg² can be broken down as follows:

• Newton (N) is defined as kg*m/s², which represents force.

• Therefore, G’s units can be expressed as (kg*m/s²) * (m²/kg²), which simplifies to Nm²/kg².

This clarification shows that the gravitational constant relates to the interaction of mass and distance, solidifying why Nm²/kg² is the appropriate SI unit. The other listed choices do not accurately represent the gravitational constant's unit as they either measure different physical quantities or do not match the derived units connected with gravitational force.