Question

Show that in SI units, the unit of G is Newton m² kg⁻². The value of G was first experimentally measured by Henry Cavendish. In SI units its value is 6.673 × 10⁻¹¹ N m² kg⁻².

Answer 1

To show the SI unit of the universal gravitational constant G, start with Newton's law of gravitation:

`F = (Gm_1m_2)/(r^2)`

Rearrange to make G the subject:

`G = (Fr^2)/(m_1m_2)`

Now substitute the SI units:

• Force, F = newton (N)
• Distance, r = metre (m)
• Mass, m = kilogram (kg)

Therefore,

Unit of G = `(N xx m^2)/(kg xx kg)`

Unit of G = N m² kg⁻²

Hence, the SI unit of the universal gravitational constant is:

N m² kg⁻²

Its accepted value is approximately:

G = 6.673 × 10⁻¹¹ N m² kg⁻²