Dimensional Formula of Newton

The dimensional formula of Newton is given by,

[M¹ L¹ T^-2]

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Newton is the SI unit of Force. Therefore, the dimensional formula of Newton is same as that of the force.

⇒ Force = Mass of body × Acceleration . . . . (1)

Since acceleration is the product of velocity and [time]^–1

Or, acceleration = [LT^-1] × [T]^-1

Therefore, the dimensions of acceleration = [M⁰ L¹ T^-2] . . . . (2)

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

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

Force (Newton) = Mass of body × Acceleration

Or, F = [M¹ L⁰ T⁰] × [M⁰ L¹ T^-2] = M¹ L¹ T^-2.

Therefore, Newton is dimensionally represented as M¹ L¹ T^-2

⇒ Check Other Dimensional Formulas:

• Dimensions of Dipole Moment
• Dimensions of Boltzmann Constant
• Dimensions of Weight
• Dimensions of Gravitational Potential Energy
• Dimensions of Universal Gas Constant