Dimensional Formula of Gravitational Potential
The dimensional formula of Gravitational Potential is given by,
[M0 L2 T-2]
- M = Mass
- L = Length
- T = Time
Gravitational Potential (V) = Work done × [Mass]-1 . . . . (1)
Since, Work done = Force × Displacement
Or, W = M × a × Displacement
W = [M1 L0 T0] × [M0 L1 T-2] × [M0 L1 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].