# Dimensions of Gravitational Potential

## Dimensional Formula of Gravitational Potential

The dimensional formula of Gravitational Potential is given by,

[M0 L2 T-2]

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Gravitational Potential (V) = Work done × [Mass]-1 . . . . (1)

Since, Work done = Force × Displacement

Or, W = M × a × Displacement

W = [ML0 T0] × [MLT-2] × [ML1 T0]

∴ The dimensional formula of work done = [M1 L2 T-2] . . . . . (2)

And, the dimensions of mass = [M1 L0 T0] . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Gravitational Potential = Work done × [Mass]-1

Or, V = [M1 L2 T-2] × [M1 L0 T0]-1 = [M0 L2 T-2].

Therefore, Gravitational Potential is dimensionally represented as [M0 L2 T-2].