# Dimensions of Gravitational Potential Energy

## Dimensional Formula of Gravitational Potential Energy

The dimensional formula of Gravitational Potential Energy is given by,

M1 L2 T-2

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Gravitational Potential Energy (G.P.E) = Mass × Acceleration due to gravity × Altitude . . . (1)

The dimensional formula of mass and altitude = [M1 L0 T0] and [M0 L1 T0] . . . . (2)

And, the dimensional formula of g = [M0 L1 T-2] . . . . (3)

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

Gravitational Potential Energy = Mass × Acceleration due to gravity × Altitude

Or, G.P.E = [M1 L0 T0] × [M0 L1 T-2] × [M0 L1 T0] = [M1 L2 T-2].

Therefore, Gravitational Potential Energy is dimensionally represented as [M1 L2 T-2].