Numford

GravitationClass 11, Gravitation

Dimensional formula of Gravitational potential

[L2 T-2]

SymbolV SI unitjoule per kilogram (J/kg)

Potential energy per unit mass. It is not the same as gravitational potential energy.

Derivation

How to get the dimensional formula of gravitational potential

  1. Start from the definition: gravitational potential = energy / mass.
  2. velocity = length / time, so velocity is [L] / [T] = [L T-1].
  3. energy = mass × velocity2, so energy is [M] × [L T-1]2 = [M L2 T-2].
  4. Put in the dimension of each part: [M L2 T-2] / [M].
  5. Add the powers of each base quantity: [L2 T-2].
Same dimensions

Quantities with the dimensions [L² T⁻²]

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

Practice

Three questions on gravitational potential

1Which of these has the same dimensions as gravitational potential?

2What is the SI unit of gravitational potential?

3Do gravitational potential and gravitational potential energy have the same dimensions?

Questions

Gravitational potential: quick answers

What is the dimensional formula of gravitational potential?

The dimensional formula of gravitational potential is [L² T⁻²]. It comes from gravitational potential = energy / mass.

What is the SI unit of gravitational potential?

The SI unit of gravitational potential is the joule per kilogram (J/kg).

Which quantities have the same dimensions as gravitational potential?

Gravitational potential shares [L² T⁻²] with latent heat. Equal dimensions do not make them the same quantity.

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