# Dimensions of Coefficient of Friction

## Dimensional Formula of Coefficient of Friction

The dimensional formula of coefficient of friction is given by,

[M0 L0 T0]

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Coefficient of friction (μ) = Frictional Force × [Normal Force]-1 . . . . (1)

Since, Force (F) = Mass × acceleration = Mass × velocity × [Time]-1

And, velocity = Displacement × [Time]-1

∴ The dimensions of Force = [M] × [LT-1] × [T]-1 = [M1 L1 T-2] . . . . (2)

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

Coefficient of friction (μ) = Frictional Force × [Normal Force]-1

Or, μ = [M1 L1 T-2] × [M1 L1 T-2]-1 = [M0 L0 T0].

Therefore, the coefficient of friction is dimensionally represented as [M0 L0 T0].

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