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 = [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].

⇒ Check Other Dimensional Formulas:

• Dimensions of Charge
• Dimensions of Reynolds Number
• Dimensions of Coefficient of Friction
• Dimensions of Surface Energy
• Dimensions of Gravitational Potential Energy