# Dimensions of Newton

## Dimensional Formula of Newton

The dimensional formula of Newton is given by,

[MLT-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 L0 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] × [MLT-2] = MLT-2.

Therefore, Newton is dimensionally represented as MLT-2