Newton’s law of universal gravitation is rep- resented by

F=GMm r2
Here F is the gravitational force, M and m are masses, and r is a length. Force has the SI units kg · m/s2.
What are the SI units of the proportionality constant G?
1. m2/(kg2 · s2) 2. m/(kg · s2) 3. m2/kg
4. N · m/s2
5. m3/(kg · s2) 6. W/m3
7. m3/(kg2 · s2) 8. kg/(m2 · s2) 9. N · m
10. J · s/kg

well, since F = ma it is kg•m/s^2

so,

kg•m/s^2 = G•kg•kg/m^2
G = kg•m/s^2 * m^2/kg•kg = m^3/kg•s^2

#5

Which you could also have easily looked up online...

The SI units of the proportionality constant G can be determined by examining the equation for Newton's law of universal gravitation:

F = GMm/r^2

In this equation, F represents the gravitational force, M and m represent masses, and r represents a length. The SI units of force are kg · m/s^2.

By rearranging the equation, we can solve for the units of G:

G = F · r^2 / (M · m)

Substituting the SI units for force (kg · m/s^2), length (m), and masses (kg) into the equation, we get:

G = (kg · m/s^2) · (m)^2 / (kg · kg)

Simplifying further:

G = (kg · m^3) / (s^2 · kg^2)

Finally, simplifying the units gives us the answer:

G has SI units of m^3/(kg · s^2)

Therefore, the correct option from the given choices is 5. m^3/(kg · s^2).