What is the value and units of the universal gravitational constant G?

What is the value and units of the universal gravitational constant G?

• A. G = 9.81 N
• B. G = 9.8 x 10^9 N m^2/kg^2
• C. G = 6.67 x 10^-11 N m^2/kg^2
• D. G = 3.00 x 10^8 N s^2/m^2

Answer: (C)

G is the number that sets how strong gravity is in Newton’s law of gravitation, linking the force between two masses to their product and their separation. The law is F = G m1 m2 / r^2, so the units of G must cancel the rest to give force in newtons. Working the units out, force is N, mass is kg, distance is m, so G must have units N m^2 / kg^2, which is also commonly written as m^3 / (kg s^2). The value is about 6.67 × 10^-11, so the standard form is G ≈ 6.67 × 10^-11 N m^2 / kg^2. The other options don’t fit because they either give the wrong magnitude or use inappropriate units. For example, 9.81 N is the weight of a 1 kg mass on Earth, not a universal constant. A value like 9.8 × 10^9 would be far too large for a universal constant. The remaining option has units that don’t match the required N m^2 / kg^2.

G is the number that sets how strong gravity is in Newton’s law of gravitation, linking the force between two masses to their product and their separation. The law is F = G m1 m2 / r^2, so the units of G must cancel the rest to give force in newtons. Working the units out, force is N, mass is kg, distance is m, so G must have units N m^2 / kg^2, which is also commonly written as m^3 / (kg s^2). The value is about 6.67 × 10^-11, so the standard form is G ≈ 6.67 × 10^-11 N m^2 / kg^2.

The other options don’t fit because they either give the wrong magnitude or use inappropriate units. For example, 9.81 N is the weight of a 1 kg mass on Earth, not a universal constant. A value like 9.8 × 10^9 would be far too large for a universal constant. The remaining option has units that don’t match the required N m^2 / kg^2.