Dimensional formula of Gravitational potential energy

How to get the dimensional formula of gravitational potential energy

1. Start from the definition: gravitational potential energy = gravitational constant × mass² / length.
2. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
3. acceleration = velocity / time, so acceleration is [L T^-1] / [T] = [L T^-2].
4. force = mass × acceleration, so force is [M] × [L T^-2] = [M L T^-2].
5. gravitational constant = force × length² / mass², so gravitational constant is [M L T^-2] × [L]² / [M]² = [M^-1 L³ T^-2].
6. Put in the dimension of each part: [M^-1 L³ T^-2] × [M]² / [L].
7. Add the powers of each base quantity: [M L² T^-2].

Quantities with the dimensions [M L² T⁻²]

• Work
• Energy
• Kinetic energy
• Potential energy
• Torque
• Torsional constant
• Strain energy
• Heat
• Internal energy
• Electric potential energy
• Work function
• Photon energy
• Binding energy

Equal dimensions do not make them the same quantity. Compare gravitational potential energy with the others in the full grid.

Three questions on gravitational potential energy

Related quantities

• g Acceleration due to gravity [L T⁻²]
• E_g Gravitational field intensity [L T⁻²]
• V Gravitational potential [L² T⁻²]
• v_e Escape velocity [L T⁻¹]